Vol. VII. No.4
Editor : B.S. Tomar
Editorial
Ever since the discovery of radioactivity by
Henry Becquerel in 1896, nuclear scientists
have been trying to unravel the mystery behind
the forces that bind the nucleonic as well as
sub-nucleonic matter together. The extensive
studies on common modes of nuclear decay, such
as, alpha, beta and gamma decay in the early
part of the twentieth century were followed by
synthesis of nuclei away from the line of stability.
These studies led to the discovery of several
exotic decay modes of nuclei, such as, one and
two proton radioactivity, cluster radioactivity,
beta delayed particles emission, double beta
decay, etc., which have not yet found detailed
description in the text books on nuclear and
radiochemistry.
The present bulletin is an attempt to
introduce the various exotic nuclear decay
modes of nuclei at an elementary level. I thank
Dr. A.Goswami who readily agreed to be the
guest editor of this thematic bulletin. My sincere
thanks are due to all the authors who despite a
short notice sent in their contributions in time. I
hope the articles in this bulletin will ignite the
minds of our young researchers in the field of
nuclear chemistry and take up research in this
exciting area.
October 2008
CONTENTS
Guest Editorial
237
Cluster Radioactivity and Related
Topics
238
Bency John
One and Two Proton Radioactivity
247
A. Goswami
Double Beta Decay – An Introduction
254
V.M. Datar
Beta-Delayed Particle Emission
260
K. Sudarshan
Non-Nucleonic Excitations in Nuclei
A.B. Santra
268
Guest Editor
Dr. A. Goswami
Radiochemistry Division
Bhabha Atomic Research Centre
Trombay, Mumbai 400 085
Guest Editorial
Dr. A. Goswami
Discovery of spontaneous emission of radiation from uranium salts by Henri Becquerel in 1896 marked
the beginning of a new era in science. The name radioactivity was proposed for this phenomenon by Marie
Curie who, along with her husband Pierre Curie, discovered two more radioactive elements Polonium and
Radium (1898). They were awarded noble prize for the discovery. Rutherford was awarded noble prize in
chemistry (1908) for his study on disintegration of radioactive elements. Subsequent discovery of atomic
nucleus by Rutherford and group displacement law by Soddy firmly established the nuclear origin of the a and b- radioactivity. Spontaneous fission as a natural decay mode was discovered after a long time in 1940.
On the theoretical side, the puzzle of a-decay was solved simultaneously by Gamow and Condon and
Gurney in the year 1928 based on the quantum mechanical tunneling effect. The same theory could explain the
phenomenon of spontaneous fission. The problem of conservation of statistics and the continuous spectrum of
b-particles could be solved by the introduction of the concept of neutrino by Pauli (1931). Incidentally, the
neutrino was discovered 22 years later in 1953 by Cowan Jr and Reines. It was Fermi who established the
theory of b-decay by introducing the concept of weak interaction, characterized by a fundamental constant
that govern the beta decay.
Since the early days, there has been a constant progress made in the accelerator technology and a large
number of radioactive isotopes have been produced artificially by variety of nuclear reactions. Also there has
been tremendous development in the detection of rare events, using separators and multiple detectors and
sophisticated pulse processing techniques. This has led to the identifications of exotic decay modes like cluster
radioactivity, one- and two proton radioactivity and beta delayed particle emissions. Three articles in this
bulletin would give a brief introduction to these recent developments. Double beta decay is another kind of rare
decay mode for which search is on for quite sometime. An article on this topic has been included to give an idea
to the readers about the kind of research activity currently pursued in this area. An article on non-nucleonic
excitations in nuclei has been included to give a glimpse of the wonder-world of particles that have been
discovered by high energy nuclear physics experiments, and how the concept of quark structure of hadrons
(baryons and mesons) have been able to explain the host of particles that have been discovered.
It is my privilege to thank the contributors to this volume who had readily agreed to our request, and
timely submitted the articles. I would also like to thank Dr. B.S. Tomar for inviting me to be the guest editor of
this volume. Finally, I hope that the readers would find the articles interesting.
October 2008
237
IANCAS Bulletin
Cluster Radioactivity and Related Topics
Dr. Bency John did his M.Sc. in Physics from University of Calicut in 1984. After
graduating from the 29th batch of BARC Training School in 1986 he joined the Nuclear
Physics Division, BARC. He completed his PhD from Mumbai University in 1999 and
Postdoctoral assignment at Texas A&M University, USA during 2000-2002. His areas
of research include Experimental Low Energy Nuclear Physics in general and Nuclear
Fission, heavy ion induced nuclear reactions, in particular.
From the early days, most familiar forms of
radioactive decay are the a, b and g decays. Some of
the early nuclear models (1930) proposed that the
nuclei are composed of a particles and electrons,
probably after observing the familiar decay
channels, and this may be the first instance for
invoking a cluster model for the nuclei.
Abstract
Discovery of cluster radioactivity a quarter
century ago has stimulated a rapid development of
experimental and theoretical investigations of the
phenomenon. Major findings of this field are
reviewed briefly. Due to certain characteristics of the
c o l d -f i s si o n o f h ea v y nu c l ei a n d th e
cold-heavy-cluster formation in quasi-fission, these
processes are also identified with the cluster
radioactivity. Study of alpha clustering in light
nuclei has enriched the field of clustering in nuclei.
These aspects are also reviewed briefly.
With the discovery of neutrons in 1932, path
was open for the liquid drop model and subsequently
for the shell model using the mean field concept
(1950). The early shell models excluded cluster
states in the nuclei, however experimental
observations compelled redevelopment of the
cluster model for light nuclei (1968). The interaction
potential between a clusters thus developed has
molecular character; the effective local potentials
are like those for Van der Waal gases. Subsequent
work has led to anti-symmetrized molecular
dynamics model(AMD, 1996) and nuclear
molecular orbital representation (1970-2007) for the
nuclei. The method of AMD has been proven to be a
powerful method to describe the cluster and shell
model like features in general nuclei.
Introduction
Discovery of radioactivity in 1896 was an
epoch making event that opened up the atomic and
the sub-atomic world. Since then several different
forms of nuclear disintegrations have been
identified, including the cluster radioactivity(1984).
The discovery of cluster radioactivity from heavy
nuclei is one of the important findings in nuclear
physics. A quantum rearrangement of large number
of nucleons from one ground state of a (A,Z) nucleon
system to two ground states of the cluster(Ae, Ze) and
the daughter nucleus(A d , Z d ) systems was
discovered by Rose and Jones[1], who measured 14C
emission from 223Ra, confirming a theoretical
prediction made earlier by Sandulescu et. al [2]. A
rapid development of experimental and theoretical
investigations was stimulated by the discovery. The
Phys ics an d A stro no my Classificatio n
Scheme(PACS) introduced a new field-23.70 +j
Heavy particle decay-for dissemination of the
results.
Recently there has been increasing interests in
Bose-Einstein Condensation (BEC) of a particles in
nuclei [3]. The phenomenon of BEC is well known
for liquid helium, and recently in dilute gases. For
systems of strong interaction, pion condensation and
kaon condensation have been proposed but have not
been confirmed experimentally [4]. Experimental
signatures for BEC of alpha particles are therefore
very important. Alpha cluster states get ‘activated’ in
low lying excited states of certain light nuclei like
12
C, 16 O and 20 Ne, if the binding energy of
Dr. Bency John, Nuclear Physics Division, Bhabha Atomic Research Centre, Mumbai 400 085;
E-mail: [email protected]
IANCAS Bulletin
238
October 2008
dozen nuclei from 221Fr to 242Cm emitting light
nuclei from 14C to 34Si, correspondingly, leaving a
daughter nucleus around 208Pb. The type of cluster
decay and the decimal logarithm of the half life in
seconds for cluster and a-decay are given for each
parent nucleus. It may be noted that the a-decay is a
v e r y d o mi n a n t mo d e i n th e s e n u c l ei .
Experimentally, one of the major problems was to
suppress the enormous a-particle background. In the
first experiment performed by Rose and Jones [1],
which ran six months in order to obtain 11 events of
the cluster decay, a silicon DE-E telescope directly
viewing the source was used. The strong a-particle
background damaged the silicon detectors after
irradiation with about 109 a/cm2 and the detectors
were replaced as and when this limit was reached. In
an experiment performed at Orsay [8], the unwanted
a-particles were deflected by a strong magnetic field
produced in the superconducting spectrometer
SOLENO and selected only 14C to reach the detector
in the focal plane. A source of about 300 times
stronger than that used by Rose and Jones was
employed so that number of days to obtain about a
dozen events were reduced to five. With this high
efficiency setup it was possible to discover [8] fine
structure in cluster decay and to perform accurate
experiments using high quality implanted sources
[9]. There were also other spectrometer setups used
for the discovery depicted in Fig.1. Solid state
nuclear track detectors were also extensively used
for investigations in this field (see for e.g. [10]) since
they can record carbon and other heavy ions
incidences while being insensitive to alpha and other
low Z ions. They are made from polyethylene
terephtalate or from a phosphate glass and are cheap
and handy. But they do not deliver information
online; only after suitable post-irradiation chemical
etching the recorded ion tracks becomes visible
under microscope for manual or computer aided
counting.
inter-cluster relative motion is almost zero or of
small positive value [5]. At cluster thresholds,
precipitation of the fermions-fluid into clusters
occurs, and due to interaction between the
a-clusters, a strongly interacting Bose-gas with
coherent properties may be formed [3]. A mixed
phase of fermions and a-particles is expected in N=Z
nuclei below the threshold. It has been pointed out
that this transition from the fermions fluid to
Bose-gas is a second order phase transition [6]. We
may observe that the study of a-clustering has
brought a large range of concepts into nuclear
physics.
The present article is organized in the
following way. A brief overview of the experimental
results in cluster radioactivity, theoretical methods
for interpreting the results, and extrapolation of the
theory to the unknown super heavy region is given in
the next section. It is followed by a discussion on the
cold fission phenomenon. Cold heavy cluster
formation in nuclear reactions and a-clustering in
light nuclei are discussed in the subsequent sections.
Cluster Radioactivity
General
Radioactive decay by emission of fragments
heavier than a-particle is a relatively recent
observation and for this historical reason such decay
is termed as cluster radioactivity. This convention
leaves a-radioactivity with its well established name
although a-particle is a good enough cluster. Many
high Z nuclei decay through the emission of heavy
particles, such as, 14C, 24Ne, 30Mg, and 34Si with T1/2
in the range of few years to 1019 years. The first
experimental identification for such a phenomenon
was accomplished by Rose and Jones[1]. A rare class
of events in the spontaneous fission where the
fissioning nucleus undergo a cold rearrangement of
the initial nucleus to the ground states of the
fragments can also be considered as a manifestation
of cluster radioactivity. A unified description of
a-decay, cluster radioactivity, and cold fission is
highly desirable and many theoretical approaches
have been proposed towards this goal.
Theoretical Models
Gross features of the cluster radioactivity
places it in an intermediate position between the
a-decay and the spontaneous fission. There are two
possible theoretical approaches for understanding
the cluster decay, either as an adiabatic fission-like
process or as a sudden two-step alpha-decay-like
Nuclear chart of experimentally determined
cluster decay modes is given in Fig.1. There are two
October 2008
239
IANCAS Bulletin
Fig. 1
Nuclear chart showing experimentally determined cluster decay modes and decimal logarithm of the
cluster and a-decay half-lives (from [7]).
process (see [11] for a topical review). The
fission-like approach has evolved into a model
called Super Asymmetric Fission (SAF ) which
treats cluster radioactivity as a dynamical mass
fragmentation process. The alpha-decay-like
approach treats cluster radioactivity as emission of
heavy cluster through the Coulomb barrier, similar
to Gamow’s theory of a-decay; including the theory
of formation of the cluster in the nucleus. A
visualization of fission-like and alpha-decay-like
mechanisms of the cluster radioactivity is given in
Fig. 2. Potentials relevant in these extreme pictures
for the decay 222Ra ® 208Pb+14C are given in Fig. 3.
One can see a huge difference between the potentials
used in the two approaches.
Fig. 2
where Q is the cluster decay energy (Q-value), m
=mAeAd/A is the reduced mass, m is the nucleon
mass, and E(R) is the interaction energy of the two
fragments separated by the distance R between
centers, Ecor is a correction energy similar to the
Strutinsky shell correction, h is the Plank constant
and Ev is the zero point vibration energy. The two
terms in the action integral K correspond to the
overlapping (Kov) and separated (Ks) fragments. The
turning points of the integral are
In the an alytical super asymmetric
fission(ASAF ) model by Poenaru et. al [12] the
half-life of a parent nucleus(A,Z) against spliting
into a cluster (Ae,Ze) and a daughter (Ad,Zd) is
calculated by using the Wentzel-Kramers-Brillouin
(WKB) semiclassical approximation.
T = [(h ln 2) / (2Ev)]exp (Kov + Ks),
K = Kov + Ks =
2 Rb
(2m{[E(R) - E cor ] - Q})1/ 2 dR
ò
R
h a
IANCAS Bulletin
Schematic diagram for fission-like and
alpha-decay-like mechanisms of the
cluster radioactivity.
240
October 2008
R3
G = Pc Fcexpæç -2ò dRK(R) ö÷
R2
è
ø
where Pc is the pre-formation probability of the
cluster in the parent nucleus, and Fc describes the
motion of the cluster between the first and second
classical turning points. The exponential factor is
known as the Gamow factor where K(R) is the wave
number given by
Fig. 3
The barriers for the decay 222Ra ®
208
Pb+14C in the fission and alpha-decay
like approaches. The fission-like approach
was computed with the proximity potential
and the alpha-decay-like approach was
computed with the real part of two very
different optical potential parameters.
K(R) = ( 2m / h 2 )|Q - V(R)|
The cluster decay half life is given by
T1/2 = h ln 2 / G
Q-values and Half-Lives
The Q value for the cluster radioactivity, which
play a very important role in their decay probability
estimation, is given in Fig.4 (left panels) for known
cluster decays. The Q values are related to the mass
difference between the parent nucleus(A,Z), the
cluster(Ae, Ze) and the daughter nucleus(Ad, Zd). The
cluster radioactivity is energetically allowed if and
only
if
the
r eleased
ener gy
Q=M(A,Z)-[Me(Ae,Ze)+Md(Ad,Zd)] is a positive
quantity, (Q >0). The atomic masses M, Me and Md
are obtained from experimental measurements. To
inspect for the shell effects, the Q-values for
different kinds of cluster decay modes versus the
neutron number of the daughter nucleus(Nd) are
plotted in Fig.4 (right panels) with points belonging
to same Zd joined with lines. In the Q-value variation
with Nd, a maximum value at the magic number
Nd=126 can be observed almost as a rule. The
variation with Zd for Zd=80-82 is, as expected,
increasing towards the magic value Zd=82 with an
exception for 23F radioactivity(almost the same
value for Z d =80 and 81). As for the clusters
themselves, they are certain neutron rich nuclei and
their nucleonic structure has also an influence.
Ra = Ri + (Rt – Ri) [(Ev + E*) / E 0b E ]1/2,
1/ 2
1 é1
ù
+ + (Q + E v + E*)E l / E 2c
ê
úû
2 ë4
Rb = R t E c
,
(Q + E v + E*)
where E* is the excitation energy concentrated in the
separation degree of freedom, Ri=R0-Re is the initial
separation distance, Rt= Re+Rd is the touching point
separation distance, Rj =r0Aj1/3 (j=0,e,d; r0=1.2249
fm) are the radii of parent, emitted, and daughter
nuclei, and E ob = Ei-Q is the barrier height before
correction. The interaction energy at the barrier top,
in presence of a non-negligible angular momentum l,
is given by
Ei = Ec + El = (e2 ZeZd / Rt) + l (l + 1) / (2 mR)
The alpha-decay like approach introduces a
pre-formation probability of the cluster in the parent
nucleus[11,13]. A quantum tunneling of the cluster
through a barrier V(R) where the V(R) is determined
as a sum of an attractive nuclear potential, a
repulsive Coulomb potential and a centrifugal
potential, is assumed. The potential V(R) is a
function of only the radial coordinate R which is the
separation between the mass center of the cluster and
mass center of the daughter nucleus. Three classical
turning points for the above potential denoted as R1,
R2 and R3 in order of increasing distance from the
origin are obtained by numerical solutions of the
equation V(R)=Q. The decay-width can be written
as
October 2008
The other important ingredient influencing the
decay half-lives is the cluster-daughter nuclear
interaction potential. The decaying particle tunnels
through this potential barrier. The fission-like and
alpha-decay like models predicts completely
different shapes for the inner part of the potential
barrier(see Fig.3). Alpha-like barriers normally are
much more narrower than the fission-like barrier and
241
IANCAS Bulletin
Fig. 4
(left panels) The Q-value as a function of parent nuclear mass number Ap. The experimental
values(circles) are obtained from experimental masses while the DEF(asterix) is a model calculation
[14]. (right panels) The Q-values for different kinds of cluster decay modes versus the neutron
number Nd of the daughter nucleus(from [7]).
TABLE 1. Cluster decay modes, Q-values,
decimal logarithm of experimental half-lives and
spectroscopic factors.
their increased penetrability is compensated by the
small values of so called spectroscopic factors. The
spectroscopic factor(S) represents the pre-formation
factor Pc and it is obtained as a ratio of the calculated
half-life to the experimental half-life. This peculiar
compensation leads to a difficulty that the measured
decay probabilities are reproduced by both the
models. Therefore, getting independent information
about the barriers, especially on their internal parts,
has been seen as a priority [15] by investigators. A
combined study of the cluster decay probability of a
nucleus and fusion or elastic scattering of its decay
products would provide new information on the
mechanism of both the cluster radioactivity and the
inverse process. To sum up the present status of
calculations, a recent paper [16] brought out a list of
cluster radio-activities together with experimental
half-lives and corresponding spectroscopic factors
as given in Table 1. The spectroscopic factors were
seen to follow a simple rule as observed in earlier
works [16].
Super Heavy Region
The cluster radioactivity is controlled by the
Q-values and barriers and the role of Z=82, N=126
IANCAS Bulletin
242
October 2008
Fig. 6
Fig. 5
Experimental and calculated (CPPM)
decimal logarithm of alpha decay half lives
for parent nuclei of Z=108-118 (from
[18]).
fission valleys in heavy nuclei, resulting in their
multi-modal fission. For example, in the PES for
252
No in length l and in mass asymmetry co-ordinate
h (minimized relative to the deformation of each
fragment (b1,b2) and the neck parameter h; h
=(A1-A2)/(A1+A2), A1and A2 are fragment mass
numbers), it can be seen that the two shell model
valleys appear mainly due to the doubly magic
structure of 132Sn and 208Pb(Fig.6) [11]. The first
valley is with strongly elongated fragments and the
second one is with nearly spherical fragments. The
strongly elongated fragments in the valley lead to
very excited fragments at scission. The spherical
fragments in the valley lead to non-excited
fragments in a cold fragmentation process known as
cold fission. Such a rearrangement of large number
of nucleons without excitation of the fragments is
made possible by introducing the neck degree of
freedom. In the framework of the two centre shell
model, it is hard to imagine that the fragments remain
non-excited in such a rearrangement. The distance
between the fragments at the scission configuration
for spherical fragments (cold fission) is much
smaller than that for the normal fission. The released
fission Q-value appear mostly as total fragment
kinetic energy (TKE) for the cold fission. Extensive
experimental and theoretical works were carried out
to confirm the multi-model nature of the fission
process. It is generally understood that the true
cold-fission events have a low probability of
occurrence (typically one out of 106 fission events).
Evidently, new experiments are needed, in which the
g-rays and neutrons from each fragment are
registered. In this way the cold fragmentation in
( 208 Pb) shell is evident in the experimentally
observed cases. One of the fundamental factors in
the study of super heavy elements is production and
characterisation of doubly magic nucleus beyond
208
Pb region, where proton number Z=114, 120, 126
and neutron number N=172, 184 have been
predicted to be magic numbers. Since it is difficult to
obtain cluster decay data systematics for super heavy
mass region, well tested models of cluster decay
should be used for predictions in unknown regions.
Compared to normal nuclei, magicity in super heavy
nuclei are expected to be fragile since the region of
enhanced shell effects are generally broad. Also, the
q u a n t u m s h e ll e n er g y ma y fa v o r s h ap e
deformations, i.e., special stability is achieved for
deformed super heavy nuclei. These aspects make
cluster decay calculations in super heavy mass
region very challenging. A quantitative microscopic
description is expected only by application of the
nuclear density functional theory currently under
development. Despite current limitations, there are
several calculations available for the spontaneous
fission and alpha decay processes. For example,
experimental and calculated alpha decay half-lives
of parent nuclei with Z=108-118 are shown in Fig.5
where calculations were done using the Coulomb
and proximity potential model [17,18].
Cold fission
Introduction of shell effects in the potential
energy surface (PES) for fission leads to multiple
October 2008
Potential energy surface for 252No nucleus
as a function of elongation l and mass
asymmetry parameter h (from [11]).
243
IANCAS Bulletin
fission could be separated from the normal hot
fission. Also characteristics of each valley could be
experimentally determined and compared with the
theoretical predictions. The study of tri-modal
fission of 264Fm is instructive[11]. The PES for 264Fm
is minimized at symmetric fragmentation (charge
and mass asymmetries equal to zero). Close to the
scission, three valleys could be observed for the
symmetric fragmentation; one valley corresponds to
a new type of fission with nearly spherical
fragments, the second valley with one fragment
spherical and the other very elongated and the third
one with both fragments strongly elongated. From
the point of view of mass distributions, the new
nearly spherical fragments mode will be very similar
to spontaneous fission. But the observed TKE
distribution had two components. The component
with high TKE is termed as Sn-radioactivity, since in
this case the spherical Sn-fragments are emitted with
almost no excitation energy. The compactness of the
scission configurations together with absence of
fragment excitation will lead to value of kinetic
energy of the fragments much higher compared to
s p o n t an e o u s f is s io n p r o c e ss , t h at a lmo s t
approaching the Q-value.
influence on the formation of the reaction products
for fusion-fission and quasi-fission processes.
Signatures for possible cluster emission from
compound nuclear excited states were discussed in
[20]. For example, in the decay of 212Po* by
a-emission, the daughter will be doubly closed
208
Pb*, which may give away all its excitation energy
as kinetic energy of a-particle and recoiling
daughter due to strong shell guided clustering
effects, thereby enhancing the average kinetic
energy of the a-particles. This hypothesis was
examined in [21] for the decay of 208Po* populated in
a heavy ion reaction. Within the experimental
uncertainties no evidence for excess kinetic energy
was found.
Alpha Clustering in Light Nuclei
As mentioned in the Introduction, the theory of
alpha clustering in light nuclei has reached a much
sophisticated level and its success with experiments
shows that alpha particle behaves as a constituent
unit in the relevant nuclear states. In understanding
of general nuclear clustering phenomena, these
theoretical methodologies will be useful and,
therefore, it is important to have survey of relevant
literature giving theoretical and experimental
results. There are several studies concentrating on
8
Be, 12C, 16O, 20Ne and such a-nuclei, (for a recent
conference proceeding on this topic, see[22])
however, here, discussion is limited to some recent
works on 12C to highlight the nature of present
studies.
Heavy Cluster Formation in Nuclear Reactions
In collision of two massive nuclei, competition
between reaction channels is strongly dependent on
the contact configuration of the interacting nuclei.
The properties of the entrance channel, such as mass
asymmetry, energy, angular momentum and
deformations have a dominant role. Moreover, the
potential energy surface which is engaged in
evolution of the intermediate nuclear system is
strongly modulated by the shell effects. The
existence of minima caused by shell effects in the
potential energy is likely to be responsible for
manifestation of clustering phenomena in different
reaction channels. In case of the cold fission (an exit
channel phenomenon) the nuclear shells with Z=50
and N=82 were found to play an important role. In
the case of the entrance channel phenomenon, the
nuclear shells with Z=28, 82 and N=50, 126 would
be determining factors. Mass and energy
distributions in quasi-fission were studied recently
[19] for presence of clustering due to shells. It was
found that clustering phenomena have a great
IANCAS Bulletin
Recently, a-p article B ose- Eins tein
condensation in light nuclei, especially in 12C and
16
O was proposed[3]. In early days, the second
excited state of 12C (7.65 MeV 0+), the famous Hoyel
state, was assigned a linear 3-a structure by
Morinaga[23]. Later, it was shown that this state
which is 0.39 MeV above the 3-a threshold, has a
well developed a-cluster structure with a 8Be-a
configuration. In 2001, Tohsaki et al. [3] conjectured
that this may be a BEC state of a-particles in that
weakly interacting three a-particles are sitting in the
lowest single particle 0s state like a gas with dilute
density distribution obeying Bose statistics. The rms
radius calculated for this BEC state is 4.29 fm far
greater than the experimental rms radius of the
244
October 2008
ground state, 2.65 fm. The dilute property of this
state had not been confirmed in a direct way till the
analysis of Ohkubo and Hirabayashi[4]. In [4], the
authors confirmed the dilute nature from the Airy
structure observed in the experimental a+12C
rainbow scattering data[24,25]. The experimentally
observed rms radius of the BEC (Hoyel) state was
4.31 fm, which is in agreement with the theoretical
value.
2.
A. Sandulescu, D.N.Poenaru and W.Greiner,
Sov. J. Part. Nucl. 11, 528 (1980).
3.
A. Tohsaki et al., Phys. Rev. Lett. 87,
192501(2001)
4.
S.Ohkubo and Y. Hirabayashi, Phys. Rev. C
70, 041602(R)(2004).
5.
K. Ikeda, H.Horiuchi and S.Saito, Prog. Theor.
Phys. , Supplement, 68, 1 (1980).
From the time of publication of [23], there have
been unsuccessful searches for a 2+ state in 12C that is
first member of a rotational band with the Hoyel state
as the band-head. Recently many new experiments
have been performed probing the triple alpha
continuum of 12C. A 2+ sate has been suggested in
two different 12C(a,a’)12C* experiments [24,26] but
at two different energies, making the question
unsettled. A recent experiment [27] using the
12
C(12C,3a) reaction presented evidence for a state
consistent with [24]. Another discussion is around
the broad 10.3 MeV state in 12C that was thought to
be the 2+ member in the rotational band for many
years. Scattering experiments provided evidence
that it is a 0+ state, and precise angular distributions
confirming the 0+ multi-polarity of this state was
obtained in [24]. The exact energy of this state,
which has got an astrophysical significance as
discussed in [28], is still not clear from the different
experiments, and efforts are continuing for
determining its energy.
6.
P. Schuck et al. Nucl.Phys. A 738 (2006) 94.
W. von Oertzen, EPJ. A 29 133(2006).
7.
D.N.Poenaru, Y.Nagame, R.A.Gherghescu
a n d W . G r e in e r , P h ys . R ev . C 6 5 ,
054308(2002).
8.
L. Br illard , A. G. E layi, E. Ho ur any,
M.Hussonnois, J.F.Le Du, L.H.Rosier and L.
Stab, C.R.Acad.Sci. Paris 309, 1105(1989)
9.
E. Hourany et al. Phys. Rev. C 52, 267(1995)
Summary
15. A.A.Ogloblin, S.P.Tretyakova, R.N.Sagaidak,
S.A.Goncharov and G.A.Pik-Pichak, Nucl.
Phys. A738, 313(2004).
10. P.B.Price, Annu. Rev. Nucl. Part. Sci., 39,
19(1989)
11. A. Sandulescu, J. Phys. G: Nucl. Part. Phys. 15,
529 (1989)
12. D.N.Poenaru, W.Greiner and R.Gherghescu,
Phys. Rev. C 47, 2030(1993)
13. Z.Ren, C.Xu and Z.Wang, Phys. Rev. C 70,
034304(2004)
14. A.Bhagwat and Y.K.Gambhir, Phys. Rev. C
71, 017301(2005)
A quarter century long study of the cluster
radioactivity has established a firm knowledge base
for the phenomenon. It emerges that the cluster
emission is not an isolated phenomenon, but has
many commonalities with the a-decay and
spontaneous fission. a-clustering in light nuclei and
heavy cold cluster formation in quasi-fission
reactions has also enriched this active field of
research. It is recognized that shell closure in one or
both fragments involved is responsible for the cold
nature of the process.
16. M. Bhattacharya and G.Gangopadhyay, Phys.
Rev. C 77, 027603(2008)
17. K.P.Santhosh, R.K.Biju and and Antony
Joseph, J. Phys. G: Nucl. Part. Phys. 35 085102
(2008).
18. K.P.Santhosh and R.K.Biju, J. Phys. G: Nucl.
Part. Phys. 36, 015107(2009).
19. M.G.Itkis, G.N.Knyazheva and E.M.Kozulin,
Int. Jour. Mod. Phys. E, 17, 2208(2008)
References
20. P.Armbruster, Rep. Prog. Phys. 62, 465(1999).
1.
21. Bency John, R.K.Choudhury, B.K.Nayak,
A.Saxena, and D.C.Biswas, Phys. Rev. C 63,
054301(2001)
H. J. Rose et al. Nature 307, 245 (1984).
October 2008
245
IANCAS Bulletin
273(1973); B.Tatischeff and I, Brissaud, Nucl.
Phys. A155, 89(1970).
22. International Journal of Modern Physics E, Vol
17, No.10(2008)
23. H. Morinaga, Phys. Lett. 21, 78(1966)78
26. M.Itoh et al., Nucl. Phys. A738 (2004)268.
24. Bency John, Y.Tokimoto, Y. –W. Lui,
H.L.Clark, X.Chen, and D.H.Youngblood,
Phys. Rev. C 68, 014305(2003).
27. M.Freer et al., Phys. Rev. C 76, 34320 (2007)
28. H.O.U.Fynbo at al., Nature 433,136 (2005).
25. A. Kiss et al., J. Phys. G 13, 1067(1987);
S.M. Smith et al., Nu cl. Ph ys. A 20 7,
IANCAS Bulletin
246
October 2008
One and Two Proton Radioactivity
Dr. Asok Goswami passed M.Sc (Chemistry) from Burdwan University and joined
BARC Training school in 1979. After passing training school, he joined
Radiochemistry Division, BARC. He obtained his Ph.D. from Mumbai University in
1992. His areas of research include nuclear fission, nuclear reactions, prompt gamma
neutron activation analysis, non destructive assay techniques, and diffusion of ions
through ion exchange membranes. He has more than 80 publications in international
journals.
MZ+1, and MZ are the atomic masses of the parent (A)
and daughter (B) nuclides, and mp and me are the
masses of proton and electron respectively, and C is
the velocity of light. In terms of binding energy, the
Qp can be written as:
A nucleus undergoes radioactive decay due to
its inherent thermodynamic instability. The study of
the classical decay modes of nucleus viz. alpha
decay, beta decay, gamma decay and spontaneous
fission decay has helped in understanding the cause
of nuclear instability in terms of composition
(neutron and proton number) and structure (internal
arrangements of nucleons in definite energy levels)
of the nucleus. Thanks to the development of
sophisticated experimental techniques for detecting
very rare events, newer decay modes have been
discovered since 1980. The unstable nuclei
exhibiting these decay modes can be classified as: (i)
one proton (1p) emitters (about 25) (ii) two proton
(2p) emitters (3) and (iii) exotic cluster emitters (C,
O, F, Ne, Mg, Si)(about 25). Well known
phenomenon like b- delayed n or p emission occurs
from the excited state of a nucleus, and is not
considered as the radioactive decay modes. The
subject of the present article is: one(1p) and two
proton (2p) radioactivity. The subject has been
extensively reviewed in reference 1 and 2.
Qp = (BZ – BZ+1)
BZ = (ZMH + Nmn – MZ) C2
Similarly, for 2p radioactivity the necessary
condition is:
Qp = (BZ – BZ+2) > 0
Why one and two proton radioactivity are so rare that
it took nearly a century after the discovery of
radioactivity by Becquerel (1996) to conclusively
prove the existence of these decay modes? The
liquid drop model of nucleus gives a straightforward
answer to this question. According to this model, a
nucleus behaves like an incompressible charged
droplet of a liquid. The stability of the droplet is
governed by attractive nuclear interactions between
the constituent (n and p) of the nucleus and the
counterbalancing force of surface tension (arises due
to finite size of the drop), Coulomb repulsion
between the protons, and by an asymmetry term that
arises due to the difference in neutron and proton
numbers in a nucleus. There is an additional term due
to pairing effect which makes even- Z even -N
nucleus more stable compared to even-Z odd-N,
odd- Z even- N and odd- Z odd –N nuclei. In order to
form a b stable nucleus, a certain equilibrium
number of protons and neutrons are needed. Thus a
plot of neutron versus proton number for the known
stable isotopes (259) gives a beta stability line along
which nuclides are b stable. Upto mass number 40,
Fundamentals of one- and two- proton Radioactivity
The 1p radioactivity can be represented as:
A®B+p
where the nucleus A decays by a proton emission to
the nucleus B. The necessary condition for a nuclide
to undergo any type of radioactive decay is that the
mass of the nuclide should exceed the sum of the
masses of all the decay products so that the Q- value
for the process is positive. For example, for 1p
radioactivity, the condition can be expressed as:
Qp = (MZ+1) – MZ – mp – me)c2 > 0
Dr. A. Goswami, Radiochemistry Division, Bhabha Atomic Research Centre, Mumbai 400 085;
E-mail: [email protected]
October 2008
247
IANCAS Bulletin
TABLE 1. 1p radioactive nuclides and their proton-decay energies, half-lives, partial half-lives and
branching ratios.
Isotope
Ep/keV
T1/2(exp)
T1/2(p)
T1/2(b)
Bp(%)
Bb(%)
53m
Co
1560
247±12 ms
17 sec
200 ms
1.5
98.5
105
Sb
478
50 sec
500 ms
1
99
109
I
813
103±5 ms
103±5 ms
250 ms
99.84
0.04
112
Cs
807
500±100 ms
500±100 ms
100 ms
99.6
0.5
113
Cs
959
28±7 ms
28±7 ms
200 ms
99.99
0.01
146
Tm
1198
72±23 ms
95 ms
300 ms
76
24
147
1051
560±40 ms
300 ms
21
79
150
1263
35±10 ms
150 ms
77
23
151
1233
85±10 ms
250 ms
70
30
1.0 sec
84
16
600 ms
60.4
0.1
Tm
Lu
Lu
156
Ta
1022
160
Re
1261
790±160 ms
46±10 ms
1.31±0.16 ms
these stable nuclides are characterized by an
approximately equal number of protons and
neutrons. Beyond this mass number, more neutrons
per proton are required to overcome the Coulomb
repulsion of protons to form a stable atomic nucleus.
(N-Z)=44 for the heaviest stable nucleus 208Pb. If
extra neutrons or protons are added to a stable
nucleus, the (n-p) equilibrium is disturbed and the
resulting nucleus decays by emission of b- or b+
particle (transformation of a neutron to proton or
vice versa) to attain stability. Why proton rich
nuclei, instead of decaying by proton emission, tend
to decay by emission of b+ particle? The reason is
that, near the beta stability line, the protons are
bound to the nucleus by nuclear force and extra
energy has to be supplied to such a nucleus (in the
form of excitation energy by way of some nuclear
reaction) to take the proton off the nucleus. In other
words, the Q- value for 1p/2p radioactivity for the
proton rich nucleus near the stability line is always
negative while that for b+ decay is positive. Hence no
proton radioactivity is possible from the ground state
of a nucleus near the stability line. However, if we
keep on adding extra protons to a nucleus, the
binding energy of the successive proton decreases
and a point is reached when the last proton’s binding
IANCAS Bulletin
energy becomes zero. Such proton excess nuclides
fall on a line called proton drip line along which the
binding energy of the last proton is zero. Further
addition of protons to such nuclide would make them
unstable to decay by proton emission. Thus, to
observe one or two proton radioactivity, one has to
prepare nuclides beyond the proton drip line by way
of nuclear reactions. The task is not easy as
experimental hurdles are too many. The production
rates for such neutron deficient nuclides are
extremely low, half-lives are short, and energies of
emitted protons are relatively small. Hence, one and
two proton radioactivity remain rare decay modes till
today. About 25 nuclides have been identified that
decay by proton emission and only 3 nuclides have
been identified that decay by 2p emission from
ground state. A representative list of 1p and 2p
radioactive nuclei are given in the Table 1 and 2
respectively.
As seen from the tables, half-lives for 1p and 2p
emitters are in the range of ms to ms and major
competitor to proton decay is b+ decay. In Table 1,
where the sum of branching ratios is not ~100%, the
remaining part goes to alpha decay. Also it is seen
that 1p emitters are mostly concentrated in the mass
248
October 2008
TABLE 2. 2p radioactive nuclides and their proton-decay energies, half-lives, partial half-lives and
branching ratios.
Isotope
2p decay-energy
(MeV)
Branching
Ratio (I2p/Ib+)
Partial
Half-life(ms)
45
1.151±0.015
0.65±0.05
3.9+-00.. 44
48
Ni
1.35±0.02
21
. +-20..17
.8
8.4 +-12
7. 0
54
Zn
1.48±0.02
3.2+-10.. 88
3.7+-21.. 20
Fe
region 100-115 (Z~50) and 140-160 (N~82)
indicating that nuclear structure can influence the
decay properties of such nuclides.
Figure 1 shows the binding energy of neutron
deficient N=80 isotones calculated using the mass
formula of Möller and Nix [3]. The isotonic binding
energy parabolas connect the odd even and
even-even isotones, respectively. The distance
between the two parabolas give the proton pairing
energy Dp. The binding energy of isotones exhibit
maximum values, and the change of the slope allows
for the positive Qp values near the maxima. Thus the
first proton unbound isotone is 149Tm(Z=69) as seen
from the figure. The Qp for the decay 151Lu ® 150Yb +
p is large enough (1.24MeV) to have a measurable
proton decay branch as seen from the table 1. It is to
be noted from the table 1 and 2 that all p emitters are
odd Z isotopes while all 2p emitters are even Z
isotopes. This can be understood from Fig. 2. The
sequential emission of two protons is possible if the
mass of the one-proton daughter nucleus is smaller
than the mass of the two-proton emitter but larger
than the mass of the two-proton daughter (left). If the
intermediate state is higher in mass than the initial
state, one-proton emission is energetically
forbidden, and the decay occurs directly to the
two-proton daughter (right). Proton pairing energy
plays a pivotal role in this. Due to the gain of
stability, the mass of the even-Z 2p emitter is smaller
than the mass of the intermediate odd-Z 1p emitter,
and therefore 1p emission cannot occur.
Binding energies of neutron deficient N=80
isotones [1].
Fig. 2
Schematic energy level diagram showing
sequential emission of two proton and
direct emission of two proton [4].
A=40-50 and as seen from Table 2, known 2p
emitters fall in this mass region.
Hence 2p emission becomes the favoured
mode of decay for such nuclei. This condition is
fulfilled for medium-mass proton-rich nuclei around
October 2008
Fig. 1
The next thing to understand is the mechanism
of 1p and 2p decay. As such it is the same as that of
a-decay. Even if a proton is unbound to a nucleus, it
249
IANCAS Bulletin
Fig. 3
Schematic representation of tunneling through the Coulomb barrier for decay by 1p and 2p emission.
For one-proton emission (left), the tunneling depends mainly on the barrier height. For two-proton
emission (right) the correlation between the two protons may influence the tunneling process [2].
has to cross a finite Coulomb barrier to come out of
the nucleus. Thus the decay is not instantaneous.
There is a finite half-life for the decay. It is
worthwhile to mention that the a particle is unbound
to 238U nucleus (Qa >0), yet 238U decays with
half-life more than billions of years due to the
existence of high Coulomb barrier for the decay.
Figure 3 shows the tunneling process involved in the
1p and 2p emission.
However unlike a-decay, observation limit for
1p and 2p radioactivity exists due to the severe
experimental limitations. Thus, with present day
experimental set-up, it is not possible to measure half
life less than about 1 ms for proton decay. On the
other hand, proton decay faces severe competition
from b+ decay, so the barrier penetration half-life
should be comparable or shorter than the b+ decay
half-life so that the proton decay branching ratio is
significant (see table 1 & 2). This sets upper limit of
the half-life to about 1 ms. Thus the chance of
observing proton decay with the partial half-life of
even a few seconds is remote. Figure 4 shows the
calculated barrier penetration half-lives for a proton
as a function of the nuclear charge and decay energy.
Fig. 4
As stated earlier, production rates for proton
emitters are extremely low, the half-lives are
extremely short, and proton energies are relatively
small. Hence, a pre-selection of the desired proton
emitters from a host of the other undesirable reaction
products, and the incident beam is necessary before
their decay properties can be studied. The GSI
separator for heavy ion reaction products (SHIP) [9]
has been used successfully to discover 151Lu and
other proton emitters. Here recoiling reaction
products from the target are separated based on
momentum and ionic charges and are implanted on a
Si detector system for detection of proton decay. The
separation time for the system is about 0.5-2 ms,
Experimental Techniques
Two different approaches have been used to
produce short lived neutron deficient isotopes near
the proton drip line: (1) Spallation reactions with
high energy proton beams [5] and (2) heavy ion
fusion reactions of neutron deficient projectile and
target nuclei [6,7]. For example, 96Ru target (97.9%
enrichment) was irradiated with 261 MeV 58Ni
projectiles at GSI to produce a proton emitter 151Lu
for the first time in 1980 [8].
IANCAS Bulletin
Barrier-penetration half-lives for a proton
as a function of the nuclear charge and the
decay energy. The half-lives are calculated
from Coulomb wave functions using the
Wigner single-particle width. The
horizontal line gives the lower detection
time limit, whereas the hatched area gives
typical b-decay half-lives [2].
250
October 2008
Results
Fig. 5
Figure 5 shows the energy spectrum of the
decay products from the heavy reaction residues
produced by irradiation of 96Ru target with 261 MeV
58
Ni projectiles. The residues were separated by
SHIP. About 100 decay events due to 1p decay of
151
Lu at 1.23MeV were recorded. The proton decay
energy was well separated from the a-lines of other
reaction products. Figure 6 shows the 2p decay
energy spectrum of 4 5 Fe from the GANIL
experiment (left) [10] exhibiting a peak at 1.14 MeV,
and GSI experiment (right) [11] showing a peak at
1.1 MeV. It is to be noted that both the experiments
observed the total energy released in the decay,
neither the individual proton energies nor their
relative emission angles. The events seen at high
energy are not due to 2p emission. As can be seen
from the figures, only a few events were recorded in
both the cases, showing the sensitivity achieved in
the experiments.
Energy spectrum showing the 151Lu proton
decay line at 1.23 MeV during the
irradiation of a 96Ru target with 261-MeV
58
Ni projectiles at SHIP[12]. a-decay lines
of other reaction products are at distinctly
higher energy.
From the point of nuclear spectroscopic
aspects and predictions of 1p radioactivity, nuclides
have been classified into several regions. Some of
them are: (1) Neutron deficient Z<50 region where
the proton drip line is relatively close to the valley of
beta stability. This region is of interest for
understanding the astrophysical rapid-protoncapture (rp) process. Figure 7 shows the proton drip
line in the region Cu-Zn that has been identified, and
a possible path of the rp process. Likely proton
emitters are also indicated in the figure. (2) The
transitional region near Sn where proton emitters
like 105 Sb, 109 I, 112,113 Cs, 146,147 Tm have been
identified. Calculations of half-lives, possible
shell-model states and the ground state deformations
have been resonably successful in this region. (3)
Neutron deficient heavy nuclei (Z>76), which have
high probability of alpha decay. Proton radioactivity
of 165,166,167Ir, 171Au and 185Bi have been reported
[10]. Interesting information regarding validity of
the existing models of nucleus is being obtained
from the study of such nucleus. Efforts are on for
identification of new 1p and 2p emitters. New
facilities giving radioactive ion-beams are coming
up which will facilitate further research in this area.
The mechanism of 2p emission is still not clear.
Study on the correlation of the protons emitted can
throw light on the process. The two-proton decay
setting lower limit of detection of proton emitter
half-lives. The suppression factor of the primary
beam is high (108-1016), allowing rare events to be
observed. Similarly Fragment Mass analyser (FMA)
at the ATLAS accelerator in Argonne National
Laboratory, which is recoil mass separator, has been
used successfully to discover the heaviest proton
emitter (185Bi) known so far.
The discovery of ground state 2p radioactivity
of 45 Fe was reported in the year 2002. The
experiments were performed at the SISSI/LISE3
facility of GANIL [10], France and FRS of GSI,
Germany [11]. 45Fe was produced by fragmentation
of a primary 58Ni beam. The detection set up for two
proton radioactivity is rather elaborate. For example,
at GSI, a Si telescope of seven elements , surrounded
by a high efficiency NaI array, was used. The 2p
radioactivity was confirmed by a series of
elimination processes of the competitive decay
modes: (1) b+ decay followed by proton emission
was eliminated by non observation of two 511 keV
gamma ray in coincidence with the proton, (2)
Smaller width of the 2p emission (ground state
emission) compared with the b+ delayed p emission,
and (3) Confirmation from daughter half-life.
October 2008
251
IANCAS Bulletin
Fig. 6
(Left) 45Fe decay-energy spectrum from the GANIL experiment exhibiting a peak at (1.14 ± 0.04) MeV
[10]. (Right) 45Fe decay-energy spectrum from the GSI experiment showing four events at 1.1(1) MeV
[11]. Both spectra also show events at higher energies.
Fig. 7
Section of the chart of nuclides in the region of interest for the astrophysical rp process. The nuclei
marked by circles have been identified at GANIL. The nuclei to the left of the dashed line are predicted
to be 1p emitters. The arrow indicates a possible route for the rp process [13].
may open an original route towards studying pairing
in the atomic nucleus. In addition, this research will
allow determination of masses for nuclei beyond the
limits of stability via the measurement of the Q
value, which then allows mass-model predictions far
IANCAS Bulletin
away from the stability line to be tested. By
comparing experimental results and theoretical
calculations, the single-particle structure of
extremely proton-rich nuclei might become
accessible. A deeper understanding of nuclear
252
October 2008
structure can only be obtained by studying nuclei far
away from stability [4].
7.
J.M. Nitschke et al. : Nucl. Instrum. Methods
206, 341 (1983).
References
8.
S. Hofmann et al. in Proc. 4th Int. Conf. on
Nuclei Far from Stability. CERN 81-09,
Geneva, 190 (1981).
9.
G. Munzenberg et al. : Nucl. Instrum. Methods
161, 65 (1979).
1.
S. Hofmann: Radiochimica Acta, 70/71, 93
(1995)
2.
Bertram blank and Marek Ploszajczak: Rep.
Prog. Phys. 71, 046301 (2008).
3.
P. Möller and J.R. Nix: At. Data and Nucl.
Data Tables 26, 165 91981).
4.
Cern Courier Dec.1, 2002.
5.
J.M. D’Auria et al. :Nucl. Phys. A301, 397
(1978).
6.
C. Bruske et al. : Nucl. Instrum. Methods 186,
61 (1981).
October 2008
10. J. Giovinazzo et al. : Phys. Rev. Lett. 89,
102501 (2002).
11. M. Pfützner et al. : Eur. Phys. J. A14, 279
(2002).
12. S. Hofmann et al. Z. : Phys. A305, 111 (1982).
13. B. Blank et al. :Phys. Rev. Lett. 74, 4611
(1995)
253
IANCAS Bulletin
Double Beta Decay – An Introduction
Dr. Vivek Datar is senior scientist at Nuclear Physics Division, BARC. He
obtained his B.Sc.(Hons) degree in Physics from Bangalore University in 1974
and Ph.D. from University of Mumbai in 1983. He did post-doctoral assignments
at Institut de Physique Nucleaire (CNRS), Orsay France (1986-1987) and at the
University of New York, Stony Brook, USA (1987-1988). His areas of work
include low energy nuclear physics in general and, tests of conservation laws and
symmetries, search for massive neutrinos, first evidence for g-decay of 4+ state in
8
Be and astrophysical S17(0) from 2H(7Be,8B)n reaction at low energy using the
7
Be radioactive ion beam at the Nuclear Science Centre (now IUAC), New Delhi.
He also helped set up a 1 m2 plastic detector array for fast neutron spectral
measurements using the time-of-flight technique. He received the N. S.
Satyamurthy Award of Indian Physics Association 1989. He is a member of the
Programme Management Committee of the India based Neutrino Observatory
(INO), a collaborative project which aims to set up a large underground
laboratory primarily for neutrino physics but which could also house other
experiments that could benefit from being deep underground. He is also the
Dean-Academic, Physical and Mathematical Sciences, BARC-HBNI and is an
Adjunct Professor in the School of Natural Sciences, TIFR
Introduction
idea was converted by Fermi to a theory [2] on the
lines of the successful field theory of quantum
electrodynamics.
Soon
after,
Maria
Goeppart-Mayer proposed a second order beta
decay process, double beta decay [3], which would
proceed at a very slow rate with typical half lives
³1017 years.
Beta decay is a process where a neutron
(proton) in a nucleus transforms to a proton
(neutron) with the simultaneous emission of an
electron (positron) and an anti-neutrino (neutrino) of
the electron type. The b- decay, for example, can be
written as
n ® p + e- + v e
Two kinds of double beta decay processes are
possible involving the emission of (1) 2b-2v ( v º
antineutrino) or (2) 2b+2n, b+EC2n and ECEC2n
where EC is the nuclear electron capture process. EC
is possible whenever b + decay is allowed
energetically but the reverse is not always true.
or, when the neutron is bound in a nucleus,
ZA
® Z+1A + e- + v e
This process can also take place, if allowed by
energy considerations viz. Q-value > 0, for a bound
proton but is energetically disallowed for a free
proton. In a related process, termed electron capture,
an inner shell electron reacts with a proton in a
nucleus producing a neutron and a mono-energetic
neutrino. The first step in understanding beta decay
was taken by Pauli [1], with his suggestion of a
neutral, light, weakly-interacting spin half particle
emitted along with beta particles. This hypothesis
explained the continuous energy spectrum of beta
particles and resolved the spin-statistics crisis. This
Two Neutrino Double Beta decay
Whenever 2n2b decay is possible it usually has
to compete with normal single neutrino beta decay.
Since it is a decay process which is much slower, by a
factor of about 1015- 1020, than single beta decay the
former would be almost impossible to observe in the
prolific background of the latter process. It is
therefore best observed in those cases where single
Dr. V.M. Datar, Nuclear Physics Division, Bhabha Atomic Research Centre, Trombay, Mumbai 400 085;
E-mail: [email protected]
IANCAS Bulletin
254
October 2008
neutrino beta decay is energetically forbidden (see
Fig. 1).
The first attempts to measure double beta decay
(DBD) used geochemical methods following
Pontecorvo’s suggestion [4]. The idea was to look
for an enhancement in the abundance of 130Xe
compared to 128Xe, in geologically old samples of
tellurium ore, due to the larger phase space for the
DBD of the 130Te compared to 128Te. Interpreting
absolute concentrations could be misleading so
ratios of the xenon isotopes 128 Xe/ 132 Xe and
130
Xe/132Xe, were measured and led to the first lower
limits on DBD half-lives [5]. These were much
improved in recent times [6]. The first laboratory
real-time observation of 2n 2b decay was made by
Elliott et al. [7]. Several cases of 2n2b decay have
Fig. 2
A typical sum energy spectrum of the two
beta particles emitted in DBD and NDBD
(neutrino less DBD).
with a maximum energy, known as the end point
energy, of Qbb.
The 2b+2n is hampered by the fact that the
relevant mass differences are such that the available
energies are < 1 MeV with the corresponding values
higher by 1.02 and 2.04 MeV, respectively, for
b+EC2n and ECEC2n decays. We will not consider
these decays further in this article although searches
for these processes, though more difficult, are of
great interest.
Zero neutrino or Neutrinoless Double Beta decay
Fig. 1
A typical level diagram for a nucleus
undergoing 2b- decay. Here b- decay is
energetically forbidden.
This decay process is of fundamental interest
since it may be the only way we might be able to
identify the true nature of the neutrino viz. whether it
is its own anti-particle (Majorana particle) or is
different from its anti-particle (Dirac particle). The
possibility of a Majorana nature [10] exists only for
neutral spin half (or spin 3/2 etc.) particles.
since been observed [8], many by the Neutrino
E t to r e M aj o r a n a O b s er v a t o r y ( N E M O )
collaboration [9].
Nuclei that can decay by 2n DBD can also
decay by 0n DBD. However this process involves
the emission, in the intermediate state, of a neutrino
by a nucleon and its absorption on another nucleon.
As mentioned above this can only occur if the
neutrino is a Majorana particle. For example, if a
neutron emits a right handed neutrino it can be
absorbed by a proton if it is left handed. This is not
possible in the presently accepted Standard Model if
the neutrino is massless. This probability is
proportional to a factor (1-bn) where bn is the speed
of the neutrino in units of the speed of light. In fact it
is likely that neutrinoless double beta decay (NDBD)
is the only way of probing the Majorana nature of the
neutrino in the foreseeable future. For the NDBD
The DBD decay width G2n2b depends on a phase
space factor and a nuclear matrix element (NME) as
G2n2b = G(Qbb, Z) êM2n ê2
where G is the phase space factor (approximately µ
Qbb9 where the latter is the mass difference between
the parent and daughter atom) and M2n the NME.
The latter can only be estimated to a factor ~ 3
implying an uncertainty of ~ 10 in the half life.
The qualitative nature of the sum energy
spectrum of the two beta particles emitted in DBD is
shown in Fig. 2. The DBD spectrum is continuous
October 2008
255
IANCAS Bulletin
TABLE 1. List of nuclei where 2b2n/2b0n DBD measurements have been made.
Parent Nucleus
Abundance
(%)
Qbb (MeV)
2b2n half-life (years)
1s error
2b0n half-life (years)
90% Confidence level
48
0.187
4271.0 4.0
(4.4 ± 0.5) ´ 1019
> 5.8 ´ 1022 [17]
76
7.8
2039.6 0.9
(1.5 ± 0.1) ´ 1021
> 1.9 ´ 1025 [11]
(2.23± 0.45) ´ 1025 1s
82
9.2
2995.0 6.0
(9.2 ± 0.7) ´ 1019
> 2.1 ´ 1021
96
2.8
3350.0 3.0
(2.0 ± 0.3) ´ 1019
100
9.6
3034.0 6.0
(7.1 ± 0.5) ´ 1018
> 5.8 ´ 1023 [9]
116
7.5
2802.0 4.0
(3.0 ± 0.2) ´ 1019
> 1.7 ´ 1023
128
31.7
868.0 4.0
(2.5 ± 0.3) ´ 1024
> 7.7 ´ 1024 [6]
130
34.5
2533.0 4.0
(9.0 ± 1.0) ´ 1020
> 3.0 ´ 1024 [16]
136
8.9
2479.0 8.0
150
5.6
3367.1 2.2
(9.1 ± 0.7) ´ 1018
238
99.275
1145.8 1.7
(2.0 ± 0.6) ´ 1021
106
1.25
2771 8
> 3.7 ´ 1020
130
0.106
2611 7
(2.2 ± 0.5) ´ 1021
2b- 2n
Ca
Ge
Se
Zr
Mo
Cd
Te
Te
Xe
Nd
U
> 4.5 ´ 1023
> 3.6 ´ 1021
b+EC 2n-bar
Cd
Ba
events a narrow peak in the sum energy spectrum of
the two beta particles at Qbb is the distinctive
signature. A typical spectrum is shown in Fig. 2. The
energy spectrum arising from NDBD is a peak at
Qbb. The higher the energy resolution of a detector
which measures this sum energy, the better is the
ability to distinguish it from the background arising
from the tail of the DBD events.
nuclear matrix element corresponds to that for 0n2b
decay. It is therefore easier to search for this decay
process in cases where the Q-value is high. For
practical reasons all the nuclei being probed are
those with Q > 2 MeV.
The NDBD decay width is given by the
equation
T1/2 = 4.2 ´ 1026 (yr) [ea/(Wns)] [Mt/(bD(E)]1/2
Following Avignone et al. [8] the sensitivity to
the 0n halflife is given by
where e is the event detection efficiency, a the
isotopic abundance, W the molecular weight of the
source material, n s the number of standard
deviations corresponding to a certain needed
precision, Mt is the product of the source mass and
exposure time, b the background counts and D(E)
defines the signal region (in the relevant energy
G0n2b = G(Qbb, Z) êM0n ê2 ámnñ2
where G is the phase space factor (approximately µ
Qbb5), M0n nuclear matrix element (NME) and ámnñ
is the effective Majorana mass of the electron
neutrino [8]. The phase space factor is µ Qbb5 and the
IANCAS Bulletin
256
October 2008
Fig. 3
underground laboratory at Gran Sasso, Italy and
IGEX [12]. The former used 11 kg of enriched 76Ge
in 5 HPGe detectors and ran for about 10 years
beginning 1990 with good data corresponding to
~72 kg.yr. The corresponding numbers for IGEX are
9 kg 76Ge over 8-9 years but with good data for ~9
kg.yr. While both collaborations put similar lower
limits on a NDBD halflife ~2 ´1025 years, translating
into an upper limit ~ 0.4 eV/c2 for the effective
Majoran a mass á m n ñ , a p a rt o f th e
Heidelberg-Moscow collaboration have claimed
positive evidence for NDBD with a quoted halflife
of about 2.2 ´1025 years at 1s implying an ámnñ of ~
0.4 eV/c2. Efforts are being mounted by the new
collaborations GERDA [13] and MAJORANA [14]
to either confirm this claim or push the sensitivity to
~ 0.13 eV/c2 and 0.06 eV/c2, respectively.
Natural abundances and Q-values for
NDBD candidate nuclei.
domain). It is clear that the lower limit on the NDBD
half life can be converted to an upper limit on ámnñ
and is µ (Mt)-1/4 . An improvement by a factor of 2
requires an increase in Mt by factor of 16!
130
Te: The first laboratory measurement [15] using a
cryogenic bolometer was made by the group of
Fiorini at Milano. The basic principle of the method
is that the specific heat of a non-magnetic insulator
varies as (T/qD)3, qD being the Debye temperature, so
that if cooled to temperatures ~ 10mK even a small
energy deposit of the order of about 2.5 MeV can be
measured through a measurable rise in temperature.
The temperature sensor is usually a neutron
irradiated Ge crystal which has a uniform and large
concentration of n- and p-type impurities. For
example, in TeO2 at 10 mK the specific heat is about
0.8 ´10-13 J/(K mol) leading to a temperature
increase ~ 0.5 mK for crystals of about 125 cm3. The
latest results from a scaled up version of the Milano
experiment, Cuoricino, used about 41 kg of TeO2
crystals [16]. The lower limit on the NDBD half life
of 1.8 ´ 1024 years leads to upper bounds on the
effective Majorana mass of the neutrino of 0.2 – 1.1
eV/c2, similar to those from the 76Ge experiments.
This experiment is being upgraded to Cuore and will
use about 700 kg of TeO2 with some of it enriched in
130
Te.
There is a variety of techniques that have been
used to search for NDBD. The methods broadly use
calorimetry, where the total energy deposited by the
2b particles is measured with good energy resolution
(up to ~0.1% as in high purity germanium detectors
enriched in 76Ge), and tracking detectors where
energy resolution is poorer but the momenta of the
beta particles are measured yielding angular
correlation information.
Of the several NDBD candidates (see Fig. 3
below and Table 1) that groups worldwide are
working on, a few illustrative examples are briefly
described below. Some of the NDBD candidate
nuclei have been studied using more than one
technique.
The main background in NDBD experiments
arises from natural radioactivity from 40K, 232Th and
238
U and daughter products from the last two
nuclides.
Tracking Experiments
Calorimetric Experiments
The NEMO collaboration uses thin metal foils,
or powders packed between thin mylar foils, as a
beta source, a set of open Geiger Muller counters in a
solenoidal magnetic field to track the two electron
trajectories and plastic scintillators coupled to
76
Ge: The first measurements were done with
sub kg natural germanium detectors and overground
experiments with modest shielding. These were
improved upon over the years culminating in the
Heidelberg-Moscow experiment [11] done in the
October 2008
257
IANCAS Bulletin
photomultiplier tubes to measure the residual
energies for calorimetry. It has measured the 2n
DBD half lives of several nuclei and set the lower
limit on the NDBD half life of many of these nuclei.
The recently completed data runs were based on a
version called NEMO-3 which used up to about 10
kg of source material, often enriched, and had energy
resolutions (FWHM) of 14-17% at 1 MeV. The
planned SuperNEMO upgrade will use up to 200 kg
source material and have an improved energy
resolution (FWHM) of 7%.
about 2%. The aimed sensitivity to the NDBD half
life is 5 ´1028 years and an ámnñ of 10 -50 meV/c2.
Another experiment is being planned by the
XAX collaboration [20] and is much more ambitious
in that it hopes to search for DBD, NDBD in 136Xe,
weakly interacting massive particles which are
candidates of dark matter which is believed to be an
important component of the universe and, using a
136
Xe depleted 129/131Xe enriched detector, the
energy spectrum of solar pp neutrinos to a precision
of 1-2%.
100
Mo: A total of about 6.9 kg of enriched 100Mo was
used in the form of thin metallic foils. The derived
upper limit on ámnñ by quoted by NEMO-3 is
between 0.6 and 1.3 eV/c2.
Outlook
In the near future the present generation of
experiments, especially the ones based on 76Ge,
130
Te, 136Xe and 150Nd should either find evidence for
NDBD or push the present upper limit on the
effective Majorana mass of ~ 0.5 eV/c2 down to
about 0.05 to 0.1 eV/c2. Some of these experiments
may also shed light on dark matter and make more
precise measurements of solar pp neutrinos.
Scintillator Based Experiments
48
Ca: An experiment using 23 natural CaF2(Eu)
scintillators, containing about 7.6 gms of 48Ca, was
performed by the Osaka group to place a lower bond
on the half life for NDBD of 48Ca. While this nucleus
has the highest DBD Q-value of about 4.3 MeV, the
natural abundance is only 0.19% making enrichment
an attractive and even necessary means of improving
the sensitivity at 90% confidence level. The present
lower limit on the NDBD half life is 5.8 ´1022 years
and 3.5 – 22 eV/c2 [17].
References
1.
W. Pauli, letter to participants of workshop at
Tubingen Dec. 4, 1930.
2.
E. Fermi, Nuovo Cim. 11, 1 (1934); Zeit. f.
Phys. 88, 161 (1934).
3.
M.Goeppart-Mayer, Phys. Rev. 48, 512
(1935).
4.
B. Pontecorvo, Phys. Lett. B 26, 630 (1968).
5.
M.G. Inghram and J.K. Reynolds, Phys. Rev.
76, 1265 ( 1949); ibid 78, 822 (1950) and T.
Kirsten et al. Phys. Rev. Lett. 20, 1300 (1968).
6.
T. Bernatowicz et al., Phys. Rev. Lett. 69
(1992) 2341; Phys. Rev. C 47, 806 (1993) and
references therein.
7.
S.R. Elliott, A. Hahn and M. K. Moe, Phys.
Rev. Lett. 59, 2020 (1987).
8.
F.T. Avignone, S.R. Elliott and J. Engel, Rev.
Mod. Phys. 80, 481 (2008).
9.
L. Vala on behalf of the NEMO3 and
S u p e r N EM O
co l la b o r a ti o n ,
arXiv:0901.0473v1 [hep-ex] 5 Jan 2009; see
also the NEMO collaboration website
http://nemo.in2p3.fr/
136
Xe: Liquid scintillators (LS) have the ability of
dissolving upto 2% of Xe. This opens the possibility
of measuring the DBD and NDBD in 136 Xe
especially by using the enriched Xe [18] and large
sized LS detectors ~ 100 -1000 tons. An experiment
of this nature is planned at Kamioka and Sudbury
Neutrino Observatory and is expected to have a
sensitivity to ámnñ of about 0.1 eV/c2.
Gas and Liquid Ionization Detectors
136
Xe: The EXO detector [19] aims to measure
NDBD using an enriched 10 ton gas or liquid phase
detector. The detector is a Time Projection Chamber
(TPC) which is a position senstive version of an
ionization counter with the additional feature that it
will tag the daughter ion 136Ba++ using the laser
fluorescence technique. The position sensitivity of
the TPC enables the spatial location of the barium
ion thereby reducing drastically potential
background. The energy resolution is expected to be
IANCAS Bulletin
258
October 2008
10. E. Majorana, Nuovo Cimento 14, 171 (1937).
15. E. Fiorini and T. Niinikoski, Nucl. Instr. and
Meth. 224, 83 (1984).
11. H. Klapdor-Kleingrothaus. et al., Eur. Phys. J.
A
12,
147
(2001);
H .V .
Klapdor-Kleingrothaus et al., Mod. Phys. Lett.
A 16, 2409 (2001). Evidence for NDBD
p r e s en t e d b y a s u b s et o f th e
Heidelberg-Moscow collaboration: H. V.
Klapdor-Kleingrothaus, A. Deitz, I. V.
Krivosheina, and O. Chkvorez, Phys. Lett. B
586,
198
(2004)
and
H.
V.
Klapdor-Kleingrothaus and I. V. Krivosheina,
Mod. Phys. Lett. A 21, 1547 (2006).
16. C. Arnaboldi et al., Phys. Rev. Lett. 95, 142501
(2005) and references therein.
17. S. Umehara et al., Phys.Rev.C78, 058501
(2008); arXiv:0810.4746v1 [nucl-ex] 27 Oct
2008.
18. R.S. Raghavan, Phys. Rev. Lett. 72, 1411
(1994); B.Caccianiga, M. Giammarchi,
Astroparticle Phys.14, 15 (2000).
12. C.E. Aalseth, Phys. Rev. D 70, 078302 (2004).
19. K. Wamba for the EXO collaboration,
arXiv:hep-ph/0210186v1 12 Oct 2002.
13. K.T. Knopfle, inv.talk at ICHEP08, arXiv:
0809.5207v2 and references therein.
20. K. Arisaka for the XAX collaboration,
arXiv:0808.3968v3 [astro-ph] 7 Jan 2009.
14. V . E . G u is e p p e, f o r t h e M a j o ra n a
Collaboration, arXiv:0811.2446.
October 2008
259
IANCAS Bulletin
Beta-Delayed Particle Emission
Dr. K. Sudarshan is gold medalist from University of Hyderabad in MSc chemistry
in 1998. He joined radiochemistry division of BARC in 1999 from the 42nd batch of
training school. He has obtained his PhD degree from Mumbai University in 2008.
His research areas include positron annihilation spectroscopy, radio analytical
techniques and heavy ion induced reactions. He has published about 30 papers in
peer-reviewed journals.
and a have been observed. Emission of smaller
particles is common and heavier systems would be
suppressed due to the coulomb barrier similar to one
encountered in cluster emission. In the limit of large
masses of the emitted fragment, the process turns
into beta-delayed fission, observed in heavy nuclei.
The case shown in Fig. 1 corresponds to the excited
state of 151Yb which can decay by emitting proton
and is called beta delayed proton emission. The
other side of the valley of stability in mass parabola
is matched by b- delayed neutron emission.
Beta decay is one of the first forms of
radioactivity observed where a nucleus transforms to
its neighbouring isobar with conversion of one
neutron to proton or proton to neutron. The mass
parabola of isobaric series of mass number A=151 is
pictorially represented as Fig. 1 [1]. Each point in
mass parabola represents the mass of the nuclei in
their ground state. No nucleus in its ground state can
get rid of energy without changing the number of
neutrons or protons. The b- and b+ emission and
electron capture (EC), together classified as beta
decay, is very common mode in which nuclei on the
mass parabola decay to their successive neighbours
until the valley of stability is reached. It can also be
seen from the figure that the beta decay energies
(difference between masses of successive atomic
number) increase rapidly with distance from the
valley of stability. The Q values involved in the beta
decays of the nuclei near the stability line are in the
range of few MeV while it can be in excess of 10
MeV for the nuclei far away from stability. As an
example, inset in Figure 1 shows the available paths
for the decay of 151Lu. The first path leads to ground
state of 151Yb by simple b+ decay, which rarely
occurs alone. Often, the beta decay leads to the
population of excited states in the daughter nuclei
which decay to ground states by emission of
gamma-rays. However, as the distance from the
stability line increases, the energy difference
between successive nuclei is very high. This leads to
situations where particle unbound excited states are
populated in beta decay and these can emit a wide
range of particles. All such decays are generally
classified as beta delayed particle emission
E x p e r ime n t al ly ma n y di f f er e n t t yp e s o f
beta-delayed particles emissions like p, 2p, n, xn, d, t
The force responsible for beta decay is called
weak force while the force which binds the nucleons
together is strong force. This strong force is also
responsible for the emission of nucleons from the
nuclei when the binding energy is insufficient. So
the time scales of particle emission are considerably
shorter than the beta decay lifetimes of their
precursors and hence usually the observed lifetimes
of these particle emissions correspond to the
lifetimes of their beta decaying precursors. It should
be mentioned that third decay path shown as particle
emission from ground state sets the limit of isotope
synthesis. If significant amount of energy is gained
by direct particle emission then it takes dominance
over the beta decay. If the nuclei have to first go
through beta decay before particle emission, the
lifetimes of the nuclei are longer and make the
synthesis and identification of those nuclei possible.
In some cases where the nuclei are unstable towards
charge particle decay, the nuclei were separated and
their properties measured as the lifetimes are longer
owing to coulomb barrier [1].
Dr. K. Sudarshan, Radiochemistry Division, Bhabha Atomic Research Centre, Mumbai 400 085;
E-mail: [email protected]
IANCAS Bulletin
260
October 2008
can be rewritten in the general form Qx = C – S where
the constants C and “separation energies” S for the
different processes are given in Table 1 (all
separation energies refer to the mother nucleus (A,Z)
for delayed a-emission a Q-value for the final
nucleus enters).
TABLE 1. Parameters in the Q-values equation
for nucleus A Z
x
C (keV)
S
bp
782
Sn
b -d
3007
S2n
b -t
9264
S3n
b -a
29860
S4n + Qb(A-4Z-1)
ECn
-782
Sp
ECd
1442
S2p
EC
3
He
6936
S3p
ECa
26731
S4p + QEC(A-4Z-3)
-
Fig. 1
Atomic masses of a series of isotopes that
have 151 nucleons (A = 151). The filled and
open symbols correspond to measured and
predicted masses respectively. The masses
are given in energy units (MeV) to
emphasize the energy released by decay
between neighboring nuclei. The only
stable isotope, 151Eu, is shown as a
darkened square. The dashed lines show
the approximate threshold at which a
neutron or proton becomes energetically
unbound by the nucleus. The inset
illustrates three possible decay channels
for the very neutron-deficient nucleus 151Lu
[1].
As seen from the formulae, the deciding factors
in the positive Q-values of beta delayed emission of
particles are the separation energies. So these
processes are more predominant in the nuclei near
the driplines where the separation energies are very
small. The nuclei in lower mass region which have
positive Q-values for beta delayed emission are
shown in Fig. 2 [3].
Though very neutron rich isotopes decay by bdelayed neutron/neutrons emission and neutron
deficient isotopes by b + /EC delayed proton
emission, it is not necessary a nuclei can emit only
one kind of beta delayed particle. One such example
is the case of 11Li which shows different beta delayed
particle emissions as given below.
The Q-value for b-delayed emission of x
number of neutrons from the nucleus of mass (A, Z)
can be written as
Qb- xn = Qb- - S xn
(
A
)
(Z + 1) = Qb-
(
A -x
)
Z - S xn
The first expression involves the Q-value of the
parent nucleus and the separation energies of the
beta-daughter, but it can be written also in terms of
the separation energies of the mother nucleus and the
Q-value of a lighter isotope [2]. A related formula
applies to b+-delayed emission of protons, one can
replace Qb- by QEC and use that Qb- = QEC - 2 mec2
The Q-value for other delayed particle-emissions
October 2008
11
3 Li 8
-b
¾¾
® 114 Be 7
10
4 Be 6 + n
10
4 Be 5 + 2n
8
3 Li 5 + t
261
(12%)
(81%)
(4%)
(0.01%)
IANCAS Bulletin
single nucleon emission (neutron or proton)
processes, multi nucleon (xn, 2p) emission
processes, composite nucleus emission (a, 3He, t, d)
processes and delayed fission.
Beta Delayed Neutron and Proton Emission
Fig. 2
The b- delayed emission of neutrons in the
neutron rich fission products with low neutron
binding energies has been well documented. The
neutrons are promptly emitted but the overall time
scale is governed by the beta decay of the delayed
neutron precursor. Because of the importance of
delayed neutrons in the reactor control, the delayed
emission in fission products has been extensively
studied. The beta delayed neutron emission rates
also play an important role in understanding the
isobaric distribution of nucleus in the r-processes
[4]. The delayed neutron emission probabilities
depend strongly on the total energy available in the
beta decay of the precursor (Qb ) and neutron
separation energies of the neutron emitter (Sn). Since
the neutron emission occurs from a region of high
level density, the beta decay to these levels can be
treated statistically. Assuming the beta strength
function to be constant above a cut of energy C and
zero below it, the delayed emission probabilities can
be approximated as [n=5]
Nuclei with N, Z £ 50 for which the Q-value
for various b-delayed particle emission
processes is positive. The left half shows
single- and multi-nucleon emission and the
right, emission of nuclei of mass number 2
and 3.
6
2 He 4
4
2 He 2
+a+n
+ 3n
(1%)
(2%)
As most of the nuclei showing these exotic
decay modes lie close to the driplines and are short
lived, the production and identification of nuclei and
measuring the various possible decay modes is a
challenging task. For a long time, thermal neutron
induced fission has been source of neutron rich
exotic nuclei. Later, deep inelastic heavy ion
reactions provided a new way producing these
isotopes. With the advancement of facilities
producing very high energy projectiles, the
projectile fragmentation has become an important
route to produce these isotopes and study their decay
properties. Due to high energies involved, the
kinematics focussing of the fragments is well suited
f o r ma g n e ti c se p a r at io n p r o c e d u r es . T h e
advancements in the high efficient and rapid
separation processes of these fragments have
enhanced the number of nuclei studied for the
various exotic decays.
æ Qb- - S n
Pn » ç
ç Q - -C
è b
n +1
The total neutron emission probabilities in different
Na and Mg isotopes are shown in Fig. 3 [5-7].
Unmoderated neutron detection methods have
limited efficiencies and the exact neutron energy
spectra are difficult to measure experimentally. The
integrated b-- dealyed neutron emission is usually
measured. This information is essential to evaluate
the level of competition taking place between
neutron capture and b-decay for those neutron-rich
nuclei of importance to the astrophysical r-process.
The b - -delayed neutron emission and
b -delayed proton emission are charge symmetric.
The production and measurement of properties of
nuclei with no neutron binding energies (dripline
nuclei) in the ground state is difficult as the neutrons
face no barrier for emission while the nuclei with
As discussed earlier, in the exotic decay of
nuclei called beta delayed particle emission, the
particles such as p, 2p, n, xn, d, t and a have been
observed. For simplicity the various beta delayed
particles emissions would be discussed in the
following sections under categories: beta delayed
IANCAS Bulletin
ö
÷
÷
ø
+
262
October 2008
Fig. 3
(a) Systematics of Si ³1 Pin for Na and Mg isotopes relative to Qb-Sn values. The solid line is drawn to
guide the eye. (b) Variation of Si ³1 Pin with the ratio (Qb-Sn)/( Qb-C) for all Na and Mg b-delayed
neutron emitters with known b-decay scheme. C is taken as the excitation energy of the first b-fed
level.
proton unbound ground states still can be identified
in favourable cases as they face the coulomb barrier
for proton emission. The study of these delayed
n u c l eo n e mi s si o n a ss u me s imp o r t an c e in
understanding the interplay of various forces that
determine these decay processes [8]. Exact
measurement of the proton energies in b+- delayed
proton decays is easier and allows precise
level-by-level spectroscopy in neutron-deficient
nuclei. The beta delayed proton decay has been used
to test the theoretical predictions of the b-decay
rates. Some typical beta-delayed proton emitters and
branching fractions are given in Table.2a. However,
it may be pointed out the there are many nuclei with
Z<N also showing the beta delayed emission of
protons and few examples are given in Table 2b.
However, these precursors have very low proton
branching ratio as compared to the proton rich nuclei
[9].
protons are observed in many nuclei [10, 11]. The
delayed emission of combination of protons and
neutrons is less common than the emission of their
composite particles. The kinematics of the particles
is decided by energy and momentum conservations.
The main interest in b-delayed multi-particle
emission is the fact that the mechanism of the
break-up is not fully determined by energy and
momentum conservation. In three body break-up
there are three binary subsystems and each
subsystem have resonances controlling the
break-up. Whether the break-up proceeds via each of
these resonances sequentially or the beta-daughter
breaks up directly into the three body continuum is
still a matter of investigation. Sequential and direct
break-up represent limiting multi-particle
mechanisms as direct processes and compound
nucleus are for nuclear-reaction mechanisms. The
observation of the emission of more than one
nucleon also provides information on the formation
of such clusters in nuclei.
Delayed Multi Particle Emission
In the beta delayed multi particle emission, the
nucleus breaks into more than two particles. In many
nuclei, the pairing energy makes many even Z nuclei
stable towards single nucleon emission and unstable
towards two neutron or proton emissions. The beta
delayed emission of more than one neutron and
October 2008
The mechanism of multiparticle emission,
whether it is simultaneous emission or sequential
can be studied by observing the energy and angular
correlations of these particles. The beta delayed
two-proton emission has been used for this purpose.
263
IANCAS Bulletin
TABLE 2a. Some proton rich nuclei showing delayed proton emission
Precursor
Production reactiona
t1/2 (msec)
Qb-Bp (MeV)b
Proton branching ratio
N odd
9
6 C3
10
B (p,2n)
127 ± 1
16.68
~1.0
13
8 O5
14
N (p,2n)
8.9 ± 0.2
15.82
0.12
O (3He, 2n)
17
10 Ne7
16
21
12 Mg9
20
25
14 Si 11
24
29
16 S13
28
33
18 Ar15
13.93
0.99
123 ± 3
10.67
0.33
3
221 ± 3
10.47
0.32
3
188 ± 4
11.04
0.47
Ne ( He, 2n)
Mg ( He, 2n)
Si ( He, 2n)
32
3
174 ± 2
9.34
0.34
3
175 ± 3
9.78
0.76
3
Ca ( He, 2n)
80 ± 2
11.77
1.0
32
16
37
20 Ca 17
36
41
22 Ti 19
40
45
24 Cr21
109 ± 1
3
S ( He, 2n)
Ar ( He, 2n)
50 ± 6
10.80
0.25
49
26 Fe23
40
S ( O,3n)
12
75 ± 10
11.00
0.60
53
28 Ni 25
40
16
45 ± 15
11.63
0.45
Ca ( Ne, 3n)
40 ± 10
13.99
0.65
Ca (24Mg, 3n)
~40
~12.2
~0.50
t1/2 (sec)
Qb-Bp (MeV)
Proton branching ratio
4.4 ± 0.4
7.14
~3.0 x 10-2
Pd (12C, 3n)
19.3 ± 0.4
5.07
~1.0 x 10-3
113
54 Xe59
Ce (p, 5pXn)
2.8 ± 0.2
7.09c
~4.0 x 10-2
115
54 Xe61
Ce (p, 5pXn)
18.0 ± 3.0
6.20
3.4 x 10-3
117
54 Xe63
Ce (p, 5pXn)
65.0 ± 6.0
4.10
2.9 x 10-5
114
55 Cs 59
La (p, 3pXn)
0.7 ± 0.2
8.20c
116
55 Cs61
La (p, 3pXn)
3.6 ± 0.2
6.43
2.7 x 10-3
118
55 Cs63
La (p, 3pXn)
16.4 ± 1.2
4.70
4.2 x 10-4
120
55 Cs65
La (p, 3pXn)
58.3 ± 1.8
2.65c
7.0 x 10-8
Ca ( C, 3n)
Ca ( O, 3n)
57
30 Zn 27
40
61
32 Ge29
40
20
TABLE 2b. Some b-delayed proton emitters with Z<N
Precursor
Production reactiona
109
52 Te57
96
16
111
52 Te59
102
Ru ( O, 3n)
117
56 Ba61
92
1.9 ± 0.2
8.08c
119
56 Ba63
92
5.3 ± 0.3
6.35
9.0 x 10-3
29.7 ± 1.5
4.70
2.0 x 10-4
121
56 Ba65
IANCAS Bulletin
Mo (32S,2p5n)
Mo (32S,2p3n)
92
Mo (32S,2pn)
264
October 2008
in a relatively cold nucleus. The proton rich isotopes
of Te, I, Xe, and Cs showing the delayed alpha
emission are shown in the Fig. 5 [16]. In many
nuclei, the beta delayed proton decay competes with
the delayed alpha decay.
Delayed Fission
The beta delayed fission may also be treated as
extreme case of particle emission. The beta delayed
fission can be represented as
b
(N,Z) ¾
¾
® (N ± 1, Z m 1) ® å (Ni , Z i )
i
Fig. 4
where the Ni and Zi refers to the neutron number and
proton number respectively, of the fission product
and the asterisk indicates the excited state populated
in beta decay. To observe considerable beta delayed
fission branching in the nuclei, the beta decay
half-lives should be shorter than the alpha or
spontaneous fission half lives of the parent. i.e. the
beta decay should be one of the major branches of
decay and the decay Q values should be higher than
the fission barrier of the daughter nucleus. The
neutron rich nuclei which are expected and observed
to show beta delayed fission are shown in Fig.6 [17].
The graph shown here is rather old. Delayed fission
has been already established in many of nuclides
shown in the region 2 (expected to show delayed
fission based on calculations) [18]. The proton rich
nuclei which have shown and expected to show the
beta delayed fission are also shown as open and
closed circles. The fission induced by neutrons has
been most studied area in the low energy fission. The
delayed fission also provides useful information on
the low energy fission of nuclides. The beta delayed
fission has been used in determining fission barriers
in many nuclei [19]. Since, the heavy elements are
formed in the nucleosynthesis by successive neutron
capture and beta decay, all the beta delayed particle
emissions play pivotal role in deciding the final
composition of the elements and their study is
necessary to understand various processes and
problems in astrophysics [20].
The distribution of individual proton
energies and the angle between them for the
2.7 MeV Q2p-peak. This corresponds to the
2p-transition from a GT-fed state in 31C1 at
7.36 MeV ending in the g.s. of 29P. The
angular distribution shows a small angular
dependence typical of a sequential decay
[12].
The studies so far point to the sequential emission of
two protons in b+-2p decay as indicated by little or no
angular correlations between the emitted particles as
shown in b+-2p decay of 31Cl [12] as shown in Fig.4.
Composite Particle Emission
The synthesis of nuclei farther from stability
line with enormously large Q values opens further
exotic decay modes. One such example is beta
delayed emission of 3He, a and tritons besides
neutrons in the decay of 11Li. Emission of such
composite particles is possible in many other nuclei
and delayed emission of alpha particles is reported in
many nuclei [13-15]. These states are situated
typically at 5-12 MeV excitation energy and are thus
bridging the gap between, on the one hand, the
ground states, which in certain cases show alpha
radioactivity, and on the other hand the compound
nuclear states near or above the Coulomb barrier,
accessible through reaction processes. The study of
the beta delayed emission of composite particles is
expected to throw light on the formation
probabilities of alpha and other composite particles
October 2008
Significant developments in the production
and separation of nuclei far from valley of stability
have increased the scope of studying the nuclei with
exotic decay modes as beta delayed particle
emission. The developments have been significant
265
IANCAS Bulletin
Fig. 5
A section of the nuclide chart with representative nuclides showing beta-delayed proton and alpha
particle emission [12]
Fig. 6
Delayed nuclear fission regions: 1 - Region of nuclei obtained; 2 – Expected neutron-rich delayed
fission region calculated from mass values. 3 - Boundary of neutron-rich delayed fission region
calculated [17].
especially in lighter mass region where the
separation techniques have reigned supreme. The
complexities associated with beta delayed
multiparticle emissions require sophisticated
i n s tr u me n t at io n t o d e ci p h e r i n f o r ma t io n
unequivocally. The complexities in the beta delayed
multiparticle emission and other exotic decay modes
are exemplified in the decay scheme of 31Ar in Fig. 7.
Many nuclei with predicted beta delayed particle
emissions are yet to be observed. The advancements
in the high intensity radioactive ion beams and
nuclear instrumentation are expected to provide the
opportunity to study many more such isotopes which
IANCAS Bulletin
would give further insight into the nuclear structure
and unanswered questions in astrophysics.
References
266
1.
J.C. Hardy, Science 227, No. 4690 (1985) 993.
2.
K. Riisager, Eur. Phys. J. A. 15 (2002) 75.
3.
B. Jonson and K. Riisager, Nucl. Phys. A. 693
(2001) 77.
4.
F. Montes et al., Phys. Rev. C 73 (2006)
035801.
5.
K.L. Kratz and G. Herrmann, Z. Phys. 263
(1973) 435.
October 2008
6.
M. Langevin et al., Nucl. Phys. A. 414 (1984)
151.
7.
K. Takahanashi, Prog. Theor. Phys. 47 (1972)
1500.
8.
C. Detraz, D. J. Vieira, Ann. Rev. Nucl. Part.
Sci. 39 (1989) 407.
9.
J. Cerny, J.C. Hardy, Ann. Rev. Nucl. Sci. 27
(1977) 333.
10. J.P. Dufour et al., Phys. Lett. B. 206 (1998)
195.
11. B. Blank et al., Nucl. Phys. A. 615 (1997) 52.
12. M.J.G. Borge et al, in International Nuclear
Physics Conference INPC 2001, Edited by E.
Norman et al., CP610.
13. P. Hornshoj et al., Phys. Lett. B. 55 (1975) 53.
14. B. Blank, J. Phys. G.: Nucl. Part. Phys. 24
(1998) 1385
15. H. Jeppesen et al. Prog. Theor. Phys. Suppl.
146 (2002) 520.
Fig. 7
Decay scheme of 31Ar and its daughters.
This figure shows the complexities in the
beta decay of an exotic nucleus. Note that
31
Ar could be two-proton radioactive, but
neither this branch nor the beta-delayed
three-proton
branches
have
been
established experimentally [3].
16. P.T. Petersson et al., Nucl Phys. A. 437 (1985)
342
17. E. Ye. Berlovich and Yu. N. Novikov, Phys.
Lett. B 29 (1969) 155.
18. D. Habs et al., Z. Phys. A. 285 (1978) 53.
19. H.V. Klapdor et al., Z. Phys. A 292 (1979) 249.
20. F.-K. Thielemann et al., Z. Phys. A 309 (1983)
301.
October 2008
267
IANCAS Bulletin
Non-Nucleonic Excitations in Nuclei
Dr. A.B. Santra joined BARC in 1978 after doing M.Sc. in Physics from IIT
Kharagpur; subsequently did Ph.D. and post-doctoral work from University of
Mumbai and University of Alberta, Canada respectively. His research interest mainly
lies in the interface areas of nuclear and particle physics. He worked on resonance
excitations in nuclear reactions, weak decays of heavy mesons, structure of neutron
stars and nuclear matter. Currently, he is interested in understanding problems of low
energy nuclear physics, saturation of nuclear matter in particular, including effects
arising from the fundamental dynamics of strong interaction.
later and named pion p. It appears in three charge
states, namely, p+, p0 and p- with almost same masses
of about 140 MeV. These three charge states behave
identically in strong interaction, so pion is assigned
isospin one. The group of strongly interacting
bosons is called mesons. Meson number need not be
conserved in a nuclear interaction. Pion is the
lightest member of meson group.
Abstract
Nuclei are complex-composite systems.
Characteristic to such systems nuclei exhibit a very
rich excitation energy spectrum. These could
involve usual nucleonic or non-nucleonic degrees of
freedom, depending on the energy scale.
Non-nucleonic degrees of freedom include various
mesonic and baryonic resonances. In this article, we
aim to discuss excitations of non-nucleonic degrees
of freedom from the quark dynamics. An exotic state
called “pentaquark” is discussed to show how
observation of such a state may open a new direction
towards understanding the strong interaction
dynamics.
Over the years, this interaction mechanism has
been extended to include the exchange of heavier
members of the meson group, such as sigma (s), rho
(r), omega (w), eta (h) and others between nucleons.
The two nucleon interacting potential, obtained
invoking meson exchange mechanism between
nucleons, is able to account extremely well all data
of nucleon-nucleon scattering experiments up to
about 400 MeV. Thus, there must be various mesons
present in a nucleus for binding the nucleons
together to form the nucleus.
Introduction
The atomic nucleus is a bound system of
neutrons (n) and protons (p) interacting through
strong interaction. Neutron and proton have mass
about 939 MeV, and behave identically in strong
interactions. These are considered to be two isotopic
spin projections of a state called nucleon with
isotopic spin 1/2. The isotopic spin (or isospin) is
conserved in strong interaction. The group of
strongly interacting fermions (half integral spin) is
called baryons. Nucleons are baryons with baryon
number (B) one.
However, in spite of this very strong
theoretical reason to expect mesons in the nucleus, it
was not easy experimentally to isolate the effects
arising from these mesonic constituents. It was even
more difficult to see their presence directly. The
clear evidence indicating presence of mesonic
effects was found in the radiative capture of thermal
neutrons in hydrogen, n + p ® d + g. Experimentally,
the cross-section is 334.2 ± 0.5 mb, whereas the best
calculations taking only nucleonic degrees of
freedom give about 302.5 mb. This discrepancy of
about 10% is now reasonably well understood in
terms of effects arising due to non-nucleonic or
mesonic degrees of freedom.
It was realized quite early that nuclei are far
more complex than just collection of neutrons and
protons. As early as in 1935, Yukawa proposed the
idea that nucleons interact through the exchange of a
boson (integral spin particles) of mass about 140
MeV. Such a particle with spin-zero was discovered
Dr. A.B.Santra, Nuclear Physics Division, Bhabha Atomic Research Centre, Trombay, Mumbai 400 085:
E-mail: [email protected]
IANCAS Bulletin
268
October 2008
There are several types of non-nucleonic
excitations in nuclei. Excitation of such degrees of
freedom in nuclei gives crucial information towards
understanding of the basic dynamics of strong
interaction. Here, we aim to discuss about two
different types of non-nucleonic excitations. This
article is organised as follows: We discuss In section
(2) about the structure of the nucleons the building
blocks of nuclei, in section (3) about the strong
interaction from the fundamental point of view, in
section (4), about excitations of free resonances, in
section (5) about the mechanism of modification of
resonances in nuclei, in section (6) about a new type
of excitation called pentaquark. Lastly in section (7)
we give a summary of the article.
Strangeness was preserved during their creation, but
not conserved in their decay. The production of these
particles is via strong interaction that conserves
“strangeness”, and decay is through “strangeness”
violating weak interaction.
Existence of conserved quantities in an
interaction is always associated with some symmetry
o f t h e i n te r a ct io n . T h e se t o f s y mme t ry
transformations constitute a “group”. Gell-Mann [2]
identified the symmetry group corresponding to the
symmetry that conserves isospin and strangeness to
be SU(3), the group of 3-dimensional unitary
matrices of determinant one. He recognized that this
symmetry group could generate natural groupings of
hadrons (strongly interacting particles), mesons and
baryons together into sets with same spin and parity
consisting of particles of isospin (I) multiplets that
differ only by strangeness (S). For example, the
baryon octet consists of, (I=1/2, S=0) two nucleons,
(I = 1, S = -1) three sigma (S), (I = 0, S = -1 ) one
lambda (L) and (I = 1/2, S = -2) two cascade (º). The
group of particles with same spin and parity actually
correspond to the states of representation space of
the SU(3) group. The members of the baryon octet
mentioned above correspond to the states of eight
dimensional representation of SU(3) group. The
fundamental representation of SU(3) is three
d i me n s io n a l , a n d h i g h er d i me n s io n a l
representations of SU(3) can be constructed from the
fundamental representation. Strangely enough, none
of the observed groups particles ever corresponded
to the fundamental representation of SU(3). This
indicates the existence of a deeper level of
elementary constituents of matter. The particles
corresponding to higher dimensional representation
of SU(3) must be composed of those corresponding
to the fundamental three dimensional representation
of SU(3)!
Structure of Nucleon
Magnetic moment of a structure-less point-like
spin 1/2 particle with mass m and charge e is eh/2m.
Neutron and proton are thus expected to have
magnetic moments 0 and 1 nuclear magneton
respectively. However, observed magnetic moments
of neutron are -1.91 and that of proton is 2.79 nuclear
magneton. Nucleons are not structure-less point-like
particles.
First experimental evidence towards internal
structure of nucleon was obtained in the 1950’s in p+
and p- scattering off the proton [1]. The scattering
cross-section, when plotted as a function of total
energy, shows a broad resonance like structure,
which is due to the formation of an intermediate
state, called delta (D), the lowest excited state of
nucleon. The mass of (D)is 1232 MeV and the width
is about 112 MeV. It decays predominantly through
the strong interaction to pion and nucleon with
lifetime of the order of 5 x 10-24 sec corresponding to
the decay width. The spin and isotopic spin of this
state have been identified to be 3/2 and 3/2
respectively.
In 1964 Gell-Mann and Zweig [3] proposed the
idea of quarks as the constituents of hadrons. It is
possible to understand all low lying hadrons with
only three spin 1/2 quarks, up (u), down (d) and
strange (s).
Within a few years after the discovery of delta,
a large number of short lived strongly interacting
particles, usually called resonances, were
discovered. Besides the excited states of nucleons,
these resonances included particles that show
“strange” behavior. These were produced copiously
but decayed slowly. Noting that production of these
particles always associated pairs, a new conserved
quantity, called “strangeness”, was postulated.
October 2008
269
Quark
Charge
(Q)
I
IZ
S
Baryon
No. (B)
u
2/3
1/2
1/2
0
1/3
IANCAS Bulletin
d
-1/3
1/2
s
-1/3
0
-1/2
0
1/3
-1
1/3
The understandings of hadrons in terms of
quarks face a problem concerning the Fermi-Dirac
statistics of the constituents. Since the fundamental
state of a composite system is expected to have zero
oribital angular momentum, the D++ baryon (J = 3/2)
corresponds to (u ­ u ­ u ­), with the three
quark-spins aligned in the same direction and all
relative angular momentum equal to zero. This wave
function is symmetric and, therefore, the D++ state
obeys the wrong statistics. The problem can be
solved [6] by assuming the existence of a new
quantum number called, color, such that each
species of quark may have three different colors, say
(red, yellow, green). One can construct an
anti-symmetric state of the D++ in which the colour
part of the wavefunction is antisymmetric. At least
three colors are needed for making an antisymmetric
state. Baryons and mesons are described by the
color-singlet combinations of quarks. Direct test of
the color quantum number, however, has been
obtained through various processes, and number of
colors has been experimentally determined to be
three.
Different types of quark are termed as flavors,
which is conserved in strong interaction but not in
weak interaction. Later three more flavors of quark,
namely, charm, beauty and top, have been
discovered. According to relativistic quantum
mechanics, corresponding to every particle there
must exist an antiparticle with same mass and
opposite charge. Quarks (q) are thus associated with
anti-quarks (q). The baryons are composed of three
quarks (q) to make, B = 1, and the mesons are with a
pair of quark (q) and antiquark (q) to make B = 0.
Quark structures of a few baryons and mesons
can be written as, p º (uud), n º (udd), D+++ º (uuu),
D+ º (uud), D0 º (udd), D- º (ddd), p+ º (ud), p0 º (uu
-dd)/ 2, p- º (du), K+ º (us), K- º (su), S+ º (uus), S- º
(dds), S 0 º (uds). There is a one to one
correspondence between the observed hadrons and
the states predicted by this simple classification;
thus, the quark model appears to be a very useful
periodic table of hadrons.
States with non-zero color have not been
observed. So, it is further postulated that all
asymptotic states are colorless, i.e. singlets under
rotations in color space. This assumption is known as
the confinement hypothesis, because it implies the
non-observability of free quarks: since quarks carry
color they are confined within color-singlet bound
states.
In the late 1960’s Friedman, Kendall and
Taylor [4] discovered quarks in their pioneering
experiment, by hitting the proton hard with electron
in the deep inelastic region where the energy transfer
(n) and the momentum transfer (Q) are very large. At
high momentum and energy transfer the elastic
collisions become very unlikely, as elastic form
factor decreases rapidly. However, the proton was
found to break up into hadron fragments. The
inelastic cross-section is very large! Proton must be
made of something more elementary. The quark
model of Gellman and Zweig got experimental
confirmation.
Strong Interaction
The baryons and mesons are made of quarks.
The strong interaction that binds nucleons to form
nuclei must be some kind of residual manifestation
of the strong interaction among quarks. The strong
interactions of quarks are due to their “color”
charges. There must be an object to exchange color
charge from one quark to the other. Each quark
carries three types of color charge, so, nine different
colored objects would be required to make all
possible change of colors of quarks. However, from
these nine, it is possible to make a combination
which is color neutral and would combine with any
color in the same way. Excluding that one we get
eight objects to mediate strong interaction between
quarks. These are called gluons, which are spin-1
T h e o b se r v e d st r u ct u r e f u n c ti o n s o f
electron-proton scattering in the deep inelastic
region showed a very peculiar property. These
depend only on one variable, x = Q2/2Mn, (with M as
the proton mass) instead of Q2 and n separately. This
is known as Bjorken scaling [5], and this can be
understood only by considering the proton to be
composed of point-like, non-interacting, spin-half
particles.
IANCAS Bulletin
270
October 2008
bosons and massless. In electromagnetic interaction
there is only one neutral photon that mediates the
interaction. In contrast, in case of strong interaction
there are eight gluons which are colored. The
interaction of quarks by exchanging gluons is
described by a theory, modeled in the similar
framework of electromagnetic interaction, is called
quantum chromodynamics, or QCD. It is a quantum
field theory in which interaction between quark and
gluon is introduced using the principle of local gauge
invariance [7].
MeV, md » 5 MeV and ms » 140 MeV In the limit, mu,
md, ms ® 0, quark dynamics has chiral symmetry
(though explicitly broken to a small extent).
However, when these quarks form a nucleon they
acquire mass of about 350 MeV (1000 MeV/3),
consequently the chiral symmetry is lost. This
situation where the symmetry possessed by the
dynamics is lost in the ground state is called
spontaneous symmetry breaking. The consequence
of spontaneous symmetry breaking is that the ground
state hosts mass less bosonic excitations called
``Goldstone Bosons’’ [9]. Thus, the chiral symmetry
is spontaneously broken in QCD, and the massless
Goldstone bosons are the spin zero negative parity
octet mesons, namely (p+, p0, p-, h, K+, K-, K0, K0).
The order parameter associated with chiral
symmetry breaking is the so-called chiral or quark
condensate. The spontaneous chiral symmetry
breaking implies that a massless (or nearly massless)
quark develops a non-zero dynamical mass.
interacting with the quark condensates. The
Goldstone bosons become the fundamental degrees
of freedom of low energy QCD. Small masses of
these Goldstone bosons is due to the fact that the
chiral symmetry was not exact but explicitly broken
by a small amount
One of the most important wisdom of
relativistic quantum theory is that, the vacuum is not
just the empty space; it can be thought of as a
medium of virtual particles. In QCD the vacuum
contains virtual quark-antiquark pairs that interact
by exchanging virtual gluons. When a quark is
placed in vacuum, its color can polarize this medium
of virtual quark-antiquark and gluon, and due to this
its colour may appear to an approaching gluon less if
the gluon has large momentum, and large if it has less
momentum. The coupling constant (or the
interaction strength) depends on the energy scale; it
is not a constant, but running. In the very high energy
limit the coupling constant becomes very small, the
quarks are non-interacting in the asymptotic limit!
This is known as asymptotic freedom [8]. On the
other hand in the low energy limit the coupling
constant grows large. This is known as infrared
slavery. Converting momentum scales to the length
scales we may say that quarks are non-interacting at
small distance scales and very strongly interacting at
large distance scales. The quarks inside the nucleon
are almost free, however, they interact very strongly
if we try to bring one of them out of the nucleon. This
explains scaling behavior in deep inelastic
scattering, and justifies the confinement hypothesis.
Spontaneous symmetry breaking is a
widespread phenomenon, and analogues exist in
various other areas of physics. In case of
paramagnetic to ferromagnetic transition the basic
hamiltonian of this spin system is invariant under
rotations in space. However, its low temperature
phase is characterized by a non-vanishing
magnetization which points into a definite direction
in space. Rotational symmetry is spontaneously
broken. This is a non-perturbative, collective
phenomenon. Many spins cooperate to form the
macroscopically magnetized material. Slow
variations in the direction of the magnetization
produce a collective low-frequency, long
wavelength motion of the spins. This spin wave
(magnon) is the Goldstone boson of spontaneously
broken rotational symmetry. In case of spontaneous
chiral symmetry breaking, the analogue of the
non-vanishing magnetization is the chiral
condensate; the analogue of the spin wave is the
octet mesons.
Quantum chromodynamics possesses another
interesting symmetry. Particles with zero mass move
with the speed of light. If the alignment of spin and
momentum (called helicity) of a mass less fermion is
fixed in one frame it will appear same from all other
frames as no frame can move faster than it. Thus
helicity of a mass less particle is conserved. It is
associated with a symmetry called chiral symmetry.
Masses of u, d and s quarks, that constitute the low
lying excitations of strong interaction physics, are
small compared to the energy scale of QCD, mu » 2
October 2008
271
IANCAS Bulletin
The main features of QCD that percolate to low
energy strong interaction physics:
taken as the fundamental feature of low energy
QCD. The basic degrees of freedom here are the
Goldstone bosons, and baryons emerge as the
solitonic excitation of the non-linear interaction
among the Goldstone bosons. These models are
known as chiral soliton models [11].
·
There are two vacuua called perturbative
vacuum and physical vacuum. Perturbative
vacuum hosts colored quarks and gluons, but
physical vacuum hosts color-less hadrons in
which quarks are confined.
· Chiral symmetry is spontaneously broken in
transition from perturbative to physical
vacuum. Perturbative vacuum is chiral
symmetric, as u, d, s quarks are almost mass-less
and physical vacuum is not because quarks
acquire mass.
Any model trying to understand strong
interaction at low energy must take into account the
above two features to be consistent with the
fundamental theory of strong interaction.
Experimentally general features of the
excitation energy spectrum of the nucleon, and the
properties of most of the baryon resonances have
been determined from pion elastic and inelastic
scattering. The baryon spectrum can be fairly well
accounted for by constituent quark model taking
three dimensional spin-independent harmonic
oscillator potential as the confining potential.
However, for a more detailed description of the
excitation energy spectrum a spin dependent
quark-quark interaction has to be included. The spin
dependent potential can be generated through one
gluon exchange or scalar meson exchange between
the quarks [12].
Free Baryons and Resonances
Formation of structure in low energy QCD can
be addressed by studying the complete spectrum of
excited states of nucleon. This includes the
determination of the quantum numbers and decay
branching ratios of the excited states as well as the
extraction of the couplings of the states to interaction
probes.
Baryons and Resonances in Nuclei
When baryonic or mesonic resonances form in
side nucleus by photo excitation or strong interaction
processes, the properties of the resonances are
modified. It might be naively expected that any
resonance structure would be broadened in a nucleus
due to many body effects comprising of Fermi
motion, collisional broadening (N*N ® N*N) and
additional decay modes (N*N ® NN). These
channels are not available for free baryon
resonances. Resonance excitation in nuclei,
however, also will be narrowed by medium effects
due to Pauli blocking final states. For example, the
decay, D ® Np is prohibited if the final state of the
nucleon is occupied.
QCD is established as a fundamental theory of
the strong interaction. In principle, one should be
able to construct strongly interacting particles and
their interaction starting from QCD. However,
realization of QCD towards this goal has not yet
been achieved completely. This is mainly because of
the fact that quark gluon coupling constant (or
interaction strength) becomes large at low energy,
and consequently perturbative techniques fail.
Numerical methods, requiring huge resources, are
being tried and considerable progress has been made
there.
However, modification of the properties of
hadrons including resonances can occur inside the
nuclear medium due to a fundamental feature of
QCD. The order parameter of the spontaneous chiral
symmetry breaking, the quark condensates, may
change inside the nuclear medium. Model
calculations show that quark condensate decreases
with increasing density and temperature of the
medium, leading to partial restoration of chiral
symmetry inside nuclear medium. Thus, in the
nuclear medium quarks are expected to have lower
constituent mass than that in a free nucleon. The
In this situation, QCD inspired models have
been introduced to understand baryons and
resonances. There are two classes of models. In one
class, quarks are taken as the basic degrees of
freedom, which are confined by a potential put by
hand. The feature of spontaneous breaking of chiral
symmetry has been considered in these models. This
model and its several variants are known as
constituent quark model [10]. In another class of
models spontaneous breaking of chiral symmetry is
IANCAS Bulletin
272
October 2008
hadron masses may be lowered inside the nuclear
medium. The meson-nucleon interaction strength
also will be modified.
strangeness. Those experiments found no
enhancements in S = +1 baryon channels.
Mass of (uudds) pentaquark (called Q+) with
spin = 1/2, isospin = 0, parity = +, strangeness = 1,
was predicted about 1800 MeV, and width around
hundreds of MeV in the constituent quark model.
However, chiral soliton model [15] predicted mass
and width of Q+ as 1530 MeV and about 15 MeV
respectively. The width prediction was the key for
the revival of experimental search for Q+, and in
2 0 0 3 f i r s t o b s e r v at io n w a s cl a ime d i n
photo-production on bound neutron in 12C, g + n ®
Q+K- ® K+nK-. The invariant mass spectra of, K+n,
shows a clear peak at, 1540 ± 10 MeV.
Experimental signatures towards this are
looked for in di-lepton (e+ e-) spectrum in heavy ion
collisions [13]. Di-leptons are mostly the decay
products of vector (spin =1) meson, such as rho
meson. Modification of rho meson mass inside the
nuclear medium would lead to the shift of peak in
dilepton spectrum and signal partial restoration of
chiral symmetry in nuclear medium. Experiments
have not been able to identify yet clearly the effect
arising from the chiral restoration in nuclear
medium.
Pentaquark
However, observation of Q+ is controversial
yet, as some experimental groups did not confirm its
own discovery. It is widely believed that
pentaquarks ``do not exist’’. In recent experiments,
it is again observed. More experiments are planned.
There are many possibilities for combining
quarks with color into colorless hadrons. However,
only two configurations of the usual mesons and
baryons have been found till now, though QCD
predicts the existence of mesons and baryons with
more co mplicated intern al structur e. The
non-conventional mesons could be made of a quark,
anti-quark and one gluon, (qqg) called hybrid, or of
three gluons, (qqg) called glueballs, or of two quarks
and two antiquarks, (qqqq) , etc. Similarly
non-conventional baryons could be made of three
quarks and a gluon, (qqqg), or four quarks and an
antiquark (qqqqq), etc.
If the existence of pentaquark is confirmed it
will change our view on strong interactions. Firstly,
quark model and its variants will be proved to be
incomplete and should be revisited for several
reasons. The traditional view of hadrons as “made
of” constituent quarks with mass ~350 MeV, cannot
explain its low mass and width. The constituent
quark models ignored two important features of
QCD namely, (1) according to quantum field theory
baryons are actually superposition of states with 3, 5,
7,…quarks, and (2) that constituent quarks have to
interact strongly with pion and kaon fields due to
spontaneous breaking of chiral Symmetry.
Baryons whose minimum quark content is four
quarks and one antiquark are called ``pentaquarks’’,
and those in which the antiquark has a different
flavor than the other four quarks are called ``exotic’’
pentaquarks. The quantum number for these states
cannot be defined by only three quarks. For example,
in non-exotic (uudss), baryon number, B= 1/3 + 1/3 +
1/3 + 1/3 - 1/3 = 1 and strangeness, S= 0 + 0 + 0 + -1 +
1 = 0; and for exotic (uudds), baryon number = 1/3 +
1/3 + 1/3 + 1/3 - 1/3 = 1 and strangeness = 0 + 0 + 0 +
0 + 1 = 1. A baryonic state with S = +1 is explicitly
exotic, and observation of such a state opens up new
direction in strong interaction physics.
Summary
A tricky point in nuclear physics, known for a
long time, is that the nucleons and mesons, the usual
hadorns that are observed in the asymptotic states are
not the basic degrees of freedom of the strong
interaction that governs the dynamics. The
fundamental degrees of freedom of strong
interaction are quarks, and the interaction of these
quarks is described by QCD in terms of exchange of
gluons between them. Hadrons are colorless
composites of quarks and low-lying excitations in
the QCD vacuum. The QCD vacuum, in which
hadronic excitations are built, thus, is not the
perturbative vacuum; also, this vacuum does not
There were searches in the 1960’s and 1970’s
mostly in bubble chamber experiments with incident
p and K beams for a baryon with positive
October 2008
273
IANCAS Bulletin
share some of the symmetries of QCD, the chiral
QCD is not manifest in the physical vacuum. The
chiral symmetry of QCD is spontaneously broken.
Chiral symmetry of QCD and its spontaneous
breaking play a very important role in understanding
the strong interaction dynamics at low energy.
Nuclei exhibit a very rich excitation spectrum.
By studying these excitation spectrum it is possible
to identify the correct low energy behavior of QCD,
the fundamental theory of strong interaction.
H. L. Anderson et al., Phys. Rev.85 (1952) 934
2.
Gell-Mann, M. and Neeman, Y. The Eightfold
Way (W.A. Benjamin Inc.) (1964).
3.
M. Gell-Mann, Phys. Lett. 8 (1964)214; G.
Zweig, CERN report No. 8182 TH 401 (1964).
4.
J. I. Friedman, R. W. Kendal, Ann. Rev. Nucl.
Sci, 22 (1972) 203.
5.
J.D. Bjorken, Phys. Rev. 179 (1969) 1547:
R.P.Feynman, Phys. Rev. Lett. 23 (1969) 1415
6.
M. Gell-Mann, Acta Phys. Austriaca Suppl. 9
(1972) 733; M. Han and Y. Nambu, Phys. Rev.
139B (1965) 1006.
IANCAS Bulletin
H. Fritzsch, M. Gell-Mann and H. Leutwyler,
Phys. Lett. 47B (1973) 365.
8.
D.J. Gross and F. Wilczek, Phys. Rev. Lett. 30
(1973) 1343, H.D. Politzer, Phys. Rev. Lett. 30
(1973) 1346.
9.
J. Goldstone, Nuov. Cim. 19 (1961) 154.
10. A. Chodos, R. L. Jaffe, K. Johnson, C. B.
T h o r n , V . W e is s k o p f , Ph y s . R e v .D 9
(1974)3471; A. Chodos, R. L. Jaffe, K.
Johnson, C. B. Thorn Phys. Rev.D10
(1974)2599
References
1.
7.
11. T. H. R. Skyrme, Proc. Royal Soc. A260
(1961)127; Nucl. Phys. 31(1962)556.
12. Ya. Glozman, D.O.Riska, Phys. Rep. 268
(1996) 263
13. G. Agakichiev et al, CERES Collaboration,
Phys. Lett. B 422, 405 (1998)
14. R. L. Jaffe, Phys.Rev.D15:267,1977,
Phys.Rev.D15:281,1977
15. D. Diakonov, V. Petrov and M. Polyakov, Z.
Phys. A 359(1997) 305
16. T Nakano et al, Phys. Rev. Lett. 91 (2003)
012002
274
October 2008